Document:

<PAGE>   1

                                                                   EXHIBIT 10.20

                               MEDIA METRIX INC.

                              AMENDED AND RESTATED

                       2000 EMPLOYEE STOCK PURCHASE PLAN

     1. Purpose.  The purpose of the Plan is to provide eligible employees of
the Company and its Subsidiaries with a means to acquire shares of the Company's
Common Stock at a discount through payroll deductions. The Plan is intended to
qualify as an "employee stock purchase plan" under Section 423 of the Code and
the Plan will be interpreted and construed accordingly.

     2. Definitions.  Wherever used herein, the following terms have the
following meanings unless a different meaning is clearly required by the
context.

          (a) "Account" shall mean the bookkeeping account established in the
     name of each Participant to reflect the payroll deductions made on behalf
     of the Participant.

          (b) "Board" shall mean the Board of Directors of the Company.

          (c) "Code" shall mean the Internal Revenue Code of 1986, as amended.

          (d) "Committee" shall mean the administrative committee appointed by
     the Board to administer the Plan.

          (e) "Common Stock" shall mean the common stock of the Company, $.01
     par value per share.

          (f) "Company" shall mean Media Metrix Inc., a Delaware corporation,
     and any successor corporation.

          (g) "Compensation" shall mean the base cash compensation paid by the
     Company or a Subsidiary to a Participant which is required to be reported
     as wages on the Participant's Form W-2, including such additional amounts
     which are not includable in gross income by reason of Sections 125, 402(e)
     or 402(h)(1)(B) of the Code, and excluding any bonuses, overtime pay,
     expense allowances and other irregular payments (except commissions).

          (h) "Employee" shall mean an individual who performs services for the
     Company or a Subsidiary in a common law employer-employee relationship.

          (i) "Enrollment Date" shall mean the first day of an Offering Period.

          (j) "Exercise Date" shall mean the last business day of an Offering
     Period.

          (k) "Fair Market Value" shall mean the closing sale price per share of
     the Common Stock as published by a national securities exchange on which
     the Common Stock is traded on such date or, if there is no sale on such
     date, on the next preceding date, or if the shares are not listed on a
     national securities exchange on such date, the average of the bid and asked
     prices in the over the counter market at the close of trading on such date.

          (l) "Offering Period" shall mean the six-month period commencing July
     1, 2000 or such later date as established by the Committee, and each
     six-month period thereafter; provided, however, that the Committee shall
     have the power to change the duration of Offering Periods and the
     commencement dates thereof without stockholder approval if such change is
     announced to Employees at least five days prior to the scheduled beginning
     of the first Offering Period resulting from such change.

          (m) "Participant" shall mean any Employee for whom an Account is
     maintained under the Plan.

          (n) "Plan" shall mean this Media Metrix Inc. 2000 Employee Stock
     Purchase Plan, as amended from time to time.
<PAGE>   2

          (o) "Subsidiary" shall mean any "subsidiary" corporation within the
     meaning of Section 424(f) of the Code that is designated by the Committee
     as a Subsidiary from time to time.

     3. Stock subject to the Plan.  Subject to the provisions of Section 11
hereof, the Company may issue and sell a total of 2,000,000 shares of its Common
Stock pursuant to the Plan. Such shares may be either authorized and unissued or
held by the Company in its treasury. The Committee may cause the Company to
purchase previously-issued and outstanding shares of Common Stock in order to
enable the Company to satisfy its obligations hereunder. The maximum number of
shares a Participant may purchase during any Offering Period shall not exceed
1,000 shares.

     4. Administration.  The Plan will be administered by a committee consisting
of at least two directors appointed by and serving at the pleasure of the Board.
Subject to the provisions of the Plan, the Committee, acting in its sole and
absolute discretion, will have full power and authority to interpret the
provisions of the Plan, to change the time covered by an Offering Period, to
supervise the administration of the Plan, and to take such other action as may
be necessary or desirable in order to carry out the provisions of the Plan. A
majority of the members of the Committee will constitute a quorum. The Committee
may act by the vote of a majority of its members present at a meeting at which
there is a quorum or by unanimous written consent. The decision of the
Committee, including questions of construction, interpretation and
administration, will be final, binding and conclusive on all persons. The
Committee will keep a record of its proceedings and acts and will keep or cause
to be kept such books and records as may be necessary in connection with the
proper administration of the Plan. The Company shall indemnify and hold harmless
each member of the Committee and any employee or director of the Company or of a
Subsidiary to whom any duty or power relating to the administration or
interpretation of the Plan is delegated from and against any loss, cost,
liability (including any sum paid in settlement of a claim with the approval of
the Board), damage and expense (including legal and other expenses incident
thereto) arising out of or incurred in connection with the Plan, unless and
except to the extent attributable to such person's fraud or wilful misconduct.

     5. Eligibility and Enrollment.  Each Employee employed by the Company or
any Subsidiary on January 13, 2000, the date of the Plan's adoption by the
Board, will be eligible to become a Participant in the Plan on the first
Enrollment Date. Each other Employee will be eligible to become a Participant in
the Plan on the Enrollment Date coincident with or next following the date he or
she completes six months of employment with the Company or a Subsidiary. An
eligible Employee will become a Participant for an Offering Period by completing
a Plan enrollment form authorizing payroll deductions and filing it with the
Company prior to the Offering Period. Payroll deductions for a Participant shall
commence with the first payroll and shall end with the last payroll in the
Offering Period to which such authorization is applicable, unless sooner
terminated by the Participant in accordance with the provisions hereof.
Notwithstanding any provisions of the Plan to the contrary, no Employee may be
granted the right to purchase Common Stock under the Plan if and to the extent
that:

          (a) immediately after the grant, such Employee would directly or
     indirectly own stock and/or hold outstanding options to purchase stock,
     possessing 5% or more of the total combined voting power or value of all
     classes of stock of the Company (determined in accordance with Section
     424(d) of the Code); or

          (b) the Employee's right to purchase stock under all employee stock
     purchase plans (within the meaning of Section 423 of the Code) of the
     Company or a Subsidiary would accrue at a rate which exceeds $25,000 in
     fair market value (determined at the time of grant) for each calendar year
     in which such right is outstanding.

     6. Payroll Deduction.  At the time a Participant enrolls in the Plan, he or
she must elect the amount to be deducted from each paycheck during the Offering
Period(s) covered by the election; provided, however, that no more than 10% of a
Participant's Compensation may be withheld under the Plan on any pay date, and
provided further that the Committee, acting in its discretion and in a uniform
and nondiscriminatory manner, may establish a minimum required amount or
percentage of Compensation which must be withheld during an Offering Period. All
payroll deductions made for a Participant shall be credited to the Participant's
Account. Interest shall not accrue on any amounts credited to a Participant's
Account. The rate of a Participant's

                                        2
<PAGE>   3

contribution, once established, shall remain in effect for all subsequent
Offering Periods unless changed by the Participant in writing at such time and
in such manner as the Committee may prescribe.

     7. Purchase of Shares.  On each Exercise Date, the amount credited to a
Participant's Account shall be used to purchase a number of shares of Common
Stock, the number of which will be determined by dividing the amount credited to
the Participant's Account by the purchase price per share. Any amount remaining
in the Participant's Account will be credited to the Participant's Account as of
the beginning of the next Offering Period. Subject to Section 11 hereof, the
purchase price per share will be equal to the lesser of 85% of the Fair Market
Value of a share of Common Stock on (i) the Exercise Date or (ii) the Enrollment
Date. If the total number of shares of Common Stock to be purchased as of an
Exercise Date, when aggregated with shares of Common Stock previously-purchased
for all Employees under the Plan, exceeds the number of shares then authorized
under the Plan, a pro-rata allocation of the available shares will be made among
the Participants based upon the amounts in their respective Accounts as of the
Exercise Date.

     8. Discontinuance or Withdrawal; Withholding Changes

     (a) Discontinuance or Withdrawal.  At any time during an Offering Period, a
Participant may notify the Company that he or she wishes to discontinue
contributions under the Plan. This notice shall be in writing and shall become
effective as soon as practicable following its receipt by the Company. A
Participant may elect to withdraw all, but not less than all, of the amount of
his or her Account at any time during an Offering Period except on the Exercise
Date with respect to that Offering Period. If a withdrawal is made during an
Offering Period, no further contributions will be permitted during that Offering
Period by the withdrawing Participant.

     (b) Withholding Changes.  At any time during an Offering Period, a
Participant may increase or decrease the rate of his or her payroll deductions
by completing or filing with the Company a new enrollment form authorizing a
change in payroll deduction rate. The Committee may, in its discretion, limit
the number of payroll deduction rate changes during any Offering Period. The
change in rate shall be effective as soon as practicable following the Company's
receipt of the new enrollment form.

     9. Termination of Employment.  Any Participant whose employment with the
Company and its Subsidiaries is terminated for any reason before an Exercise
Date shall thereupon cease being a Participant. The total amount credited to the
Participant's Account during the Offering Period will be returned to the
Participant or, in the case of a deceased Participant, to the Participant's
beneficiary, as soon as practicable after the Participant's termination of
employment.

     10. Rights as a Stockholder.  No shares of Common Stock will be issued
under the Plan until full payment therefor has been made. A Participant will
have no rights as a stockholder with respect to any shares until the date a
stock certificate for such shares is issued to him or her. Except as otherwise
specifically provided herein, no adjustments shall be made for dividends or
distributions of other rights for which the record date is prior to the date
such stock certificate is issued.

     11. Capital Changes; Reorganization; Sale.

     (a) Adjustments Upon Changes in Capitalization.  The number and class of
shares of Common Stock which may be issued under the Plan, as well as the number
and class of shares of Common Stock and the price per share covered by each
right outstanding under the Plan which has not yet been exercised, shall be
adjusted proportionately or as otherwise appropriate to reflect any increase or
decrease in the number of issued shares of Common Stock resulting from a
split-up or consolidation of shares or any like capital adjustment, or the
payment of a stock dividend, and/or to reflect a change in the character or
class of shares covered by the Plan arising from a readjustment or
recapitalization.

     (b) Cash, Stock or Other Property for Stock.  Except as otherwise provided
in this Section, in the event of an Exchange Transaction (as defined below),
each Participant will be permitted to purchase Common Stock with the balance of
his or her Account immediately prior to such Exchange Transaction, and any
amount credited to a Participant's Account which is not used to purchase Common
Stock before the Exchange Transaction will be distributed to the Participant.
Notwithstanding the preceding sentence, (i) if, as

                                        3
<PAGE>   4

part of the Exchange Transaction, the stockholders of the Company receive
capital stock of another corporation ("Exchange Stock") in exchange for their
shares of Common Stock (whether or not such Exchange Stock is the sole
consideration), and if the Board, in its sole discretion, so directs, then the
rights of all Participants to purchase shares of Common Stock will be converted
into rights to purchase shares of Exchange Stock on an economically equivalent
basis; and (ii) the Board, acting in its discretion, may suspend operation of
the Plan as of any date that occurs after a contract is made which, if
consummated, would result in an Exchange Transaction and before the Exchange
Transaction is consummated.

     (c) Definition of Exchange Transaction.  For purposes hereof, the term
"Exchange Transaction" means a merger (other than a merger of the Company in
which the holders of Common Stock immediately prior to the merger have the same
proportionate ownership of Common Stock in the surviving corporation immediately
after the merger), consolidation, acquisition of property or stock, separation,
reorganization (other than a mere reincorporation or the creation of a holding
company), liquidation of the Company or any other similar transaction or event
so designated by the Board in its sole discretion, as a result of which the
stockholders of the Company receive cash, stock or other property in exchange
for or in connection with their shares of Common Stock.

     (d) Determination of Board to be Final.  All adjustments under this Section
11 shall be made by the Board, and its determination as to what adjustments
shall be made, and the extent thereof, shall be final, binding and conclusive.

     12. Amendment and Termination.  The Board may amend or terminate the Plan
at any time; provided, however, that, except as otherwise provided in Section 11
hereof, any amendment which would increase the aggregate number of shares of
Common Stock which may be issued under the Plan or otherwise require stockholder
approval under applicable law shall be subject to the approval of the Company's
stockholders.

     13. Transferability.  The rights of a Participant to purchase Common Stock
under the Plan are not assignable or transferable and may only be exercised
during the Participant's lifetime by the Participant. A Participant may file a
written designation of a beneficiary who is to receive the amount credited to
the Participant's Account in the event of the Participant's death during an
Offering Period. A Participant's beneficiary designation may be changed by the
Participant at any time by written notice. In the event of the death of a
Participant and in the absence of a validly designated beneficiary who is living
at the time of the Participant's death, the Participant's estate will be deemed
to be his or her designated beneficiary.

     14. No Rights Conferred.  Nothing contained in the Plan shall be deemed to
give any individual any right to be retained in the service or employ of the
Company and its Subsidiaries or to interfere with the right of the Company and
its Subsidiaries to discharge him or her at any time.

     15. Use of Funds.  All payroll deductions received or held by the Company
under the Plan may be used by the Company for any corporate purpose, and the
Company shall not be obligated to segregate such payroll deductions.

     16. Legal Requirements.  The Committee may impose such other conditions
with respect to the purchase of Common Stock hereunder, including, without
limitation, any conditions relating to the application of federal or state
securities laws and/or any exchange or listing requirements as it may deem
necessary or advisable.

     17. Governing Law.  The Plan and each option agreement shall be governed by
the laws of the State of Delaware without regard to its conflict of laws
provisions.

     18. Decisions and Determinations.  Any decision or determination made by
the Board pursuant to the provisions hereof and, except to the extent rights or
powers under the Plan are reserved specifically to the discretion of the Board,
all decisions and determinations of the Committee are final, binding and
conclusive.

     19. Stockholder Approval.  The Plan shall be effective upon its adoption by
the Board, subject to approval by the stockholders of the Company within twelve
months from the date of adoption by the Board.

                                        4<PAGE>   1
                                                                  EXHIBIT 10.1.2

                   SECOND AMENDMENT TO THE TRANSFER AGREEMENT
                        BETWEEN UCAR CARBON COMPANY INC.
                            AND UCAR GRAPH-TECH INC.

        The Transfer Agreement is hereby amended, in accordance with the
following.

         1.       The second paragraph of Section 4.1 is hereby amended to read
                  in its entirety as follows:

                  "Transferee and its participating subsidiaries hereby agree to
                  be, and from and after the Closing shall continue to be, (1)
                  jointly and severally liable with Transferor and its other
                  participating subsidiaries and affiliates for all benefits
                  owed to participants and their beneficiaries under the Program
                  and the Plan and (2) except as otherwise expressly provided in
                  the Services Agreement, solely liable and responsible for all
                  benefits owed to its employees and retirees, and their
                  beneficiaries, under such plans. Subject to the parties'
                  obligations under clause (1) of the preceding sentence (which
                  the parties expect would not become applicable unless either
                  party is unable to meet its obligations under this sentence),
                  the parties agree that funding, contribution, expense and
                  other costs and payments in respect of the Plan and the
                  Program shall be borne in proportion to the obligations to
                  their respective retirees and employees. The parties agree
                  that all employees of Transferor who retired from the Business
                  after February 25, 1991 (approximately 20 employees), and
                  employees of Transferee and its subsidiaries (including the
                  Employees) who retire after the Closing, shall be considered
                  retirees of Transferee for all purposes (including, but not
                  limited to, funding obligations and administration of
                  benefits) under the Program, the Plan and such plans.
                  Notwithstanding anything contained herein or in the Services
                  Agreement to the contrary, the only assets to be transferred
                  to or for the benefit of Transferee or its subsidiaries or its
                  employee benefit plans in respect of the Program, the Plan or
                  any of such plans shall be those required to be transferred by
                  applicable law in respect of the Program or the Plan at such
                  time as Transferee or its subsidiaries ceases to participate
                  in the Program or the Plan."

         Date: July 24, 2000

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00012-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00012-of-00352.parquet"}]]