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                                                                   Exhibit 10.57

                            APPLIEDTHEORY CORPORATION
                            1500 BROADWAY, 3RD FLOOR
                               NEW YORK, NY 10036


                                 January 9, 2001


To the Investors on the Attached Schedule I:

         RE:      LETTER AGREEMENT RE DISTRIBUTION OF NEW DOCUMENTS
                   (THE "DISTRIBUTION")

         Enclosed please find the following documents (together with this letter
agreement, the "NEW TRANSACTION DOCUMENTS") in connection with that certain
Purchase Agreement (the "ORIGINAL PURCHASE AGREEMENT") entered into as of June
5, 2000 between AppliedTheory Corporation (the "COMPANY") and the investors on
the attached distribution list (the "INVESTORS"):

                  (a) an Amended and Restated Purchase Agreement dated as of
June 5, 2000 between the Investors and the Company (the "PURCHASE AGREEMENT")
executed by the Company and to be signed by the Investors and which shall, upon
full execution, supersede the Original Purchase Agreement;

                  (b) an Amended and Restated Registration Rights Agreement
dated as of June 5, 2000 between the Investors and the Company (the
"REGISTRATION RIGHTS AGREEMENT") executed by the Company and to be signed by the
Investors which shall, upon full execution, supersede the original Registration
Rights Agreement of even date (the "ORIGINAL REGISTRATION RIGHTS AGREEMENT");

                  (c) new Initial Warrants issued by the Company which shall,
upon each Investor's acceptance, replace the Initial Warrants issued to each
such Investor (collectively, the "ORIGINAL INITIAL WARRANTS"); and

                  (d) new Debentures issued by the Company which shall, upon
each Investor's acceptance, replace the Debentures issued to each such Investor
(the "ORIGINAL DEBENTURES" and collectively with the Original Purchase
Agreement, the Original Registration Rights Agreement and the Original Initial
Warrants, the "ORIGINAL TRANSACTION DOCUMENTS").

In addition, enclosed is an original of the legal opinion issued by independent
counsel of the Company in connection with the issuance of the New Transaction
Documents, in the form and substance as agreed to by your counsel, and an
officer's certificate from the Company, in form and substance substantially
similar to Exhibit 4.2(g) of the original Purchase Agreement.

Unless expressly provided to the contrary, undefined terms contained herein
shall have the meaning set forth in the Purchase Agreement, the Debentures or
the Initial Warrants.


         1. WAIVER OF RIGHTS AND REMEDIES. Each of the Investors severally and
not jointly, and the Company, acknowledges that the closing of the transactions
contemplated by the New
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Transaction Documents (the "New Closing") shall constitute a waiver of any of
such party's rights and remedies under any of the Original Transaction
Documents, including but not limited to, remedies available to the Investors in
connection with the Company's failure to cause the Registration Statement to
become effective on or before the time periods (October 3, 2000 and November 2,
2000) set forth in paragraphs (A) and (B) of Section 2(b)(i) of the Original
Registration Rights Agreement. In no event shall the foregoing be construed in
any way to limit the rights and remedies available to any Investor under any of
the New Transaction Documents, even in the event that such rights and remedies
are duplicative of the rights and remedies that were once available under the
Old Transaction Documents. The Company acknowledges that the Investors have paid
the Purchase Price in full.

         2. PRICES. The Company and the Investors agree on the following: (a) in
the new Debentures, the Closing Price is referred to as being equal to $13.35
and the Initial Conversion Price is referred to as being equal to $16.69 and (b)
in the Initial Warrants, the Exercise Price is referred to as being equal to
$6.00, in each case subject to adjustment. Except for the Exercise Price, such
prices are based on the Closing Date of June 5, 2000.

         3. 144 HOLDING PERIOD. Upon receipt of a legal opinion from the
Investors' counsel to the Company, in the form attached hereto as Exhibit A or
in such other form that is reasonably acceptable to the Company, the Company
acknowledges that, consistent with the Investors' belief, the Company will
recognize that all of the Initial Warrants and Debentures have a Rule 144
holding period under the Securities Act that commenced on June 5, 2000 for all
purposes and further acknowledges that the Company will act in accordance with
that position.

         4. PRESS RELEASE AND FORM 8-K. Promptly following the New Closing, the
Company shall issue a press release in form and substance reasonably
satisfactory to the Investors. If the Company fails to issue a press release
within two (2) business days of the New Closing, the Investors may issue a press
release covering the New Closing and complying with any legal requirements
applicable to one or more of the Investors. In addition, within 17 calendar days
of the New Closing, the Company shall file a Form 8-K with the SEC which
discloses the transactions contemplated by the New Transaction Documents. The
Investors shall have the opportunity to review such Form 8-K prior to its
filing.

         5. TRANSFER. The Company hereby recognizes the transfer of all of the
rights, title, obligations and interest of Gleneagles Fund Company
("GLENEAGLES") in connection with the Original Transaction Documents to DeAM
Convertible Arbitrage Fund, Ltd. ("DeAM"), which occurred subsequent to the
Closing Date. For convenience purposes, the Company has agreed to issue the new
Initial Warrants and new Debentures to DeAM (rather than Gleneagles) and to have
DeAM (rather than Gleneagles) be a party to the Purchase Agreement and
Registration Rights Agreement, all as of June 5, 2000.

         6. SEC FILING. The Company shall file the amended Registration
Statement prepared in connection with the New Transaction Documents within 17
calendar days of the date hereof.

         7. INDEMNITY. The Company shall indemnify each of the Investors and
Gleneagles against any loss, cost or damages (including reasonable attorney's
fees and expenses but excluding consequential damages) incurred as a result of
the Company's breach of any
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representation, warranty, covenant or agreement in this letter agreement; or
incurred as a result of the enforcement of this indemnity.

         8. EVENT OF DEFAULT. The Company hereby agrees that a breach of or
default under this letter agreement by the Company shall constitute an Event of
Default (as defined in the Debentures) under the Debentures.

         9. PERMITTED INTERIM INVESTMENTS. As of September 30, 2000, Permitted
Interim Investments equal approximately $11,800,000.

         10. DUE AUTHORIZATION. The Company hereby represents and warrants to
each of the Investors as of the date hereof that the Company has all requisite
corporate power and authority to enter into and perform this letter agreement,
the other New Transaction Documents and the transactions contemplated hereby and
thereby. The Company further represents and warrants that this letter agreement
and the other New Transaction Documents constitute valid and binding obligations
of the Company enforceable against the Company in accordance with their terms,
except as such enforceability may be limited by applicable bankruptcy,
insolvency, reorganization, moratorium, liquidation or similar laws relating to,
or affecting generally the enforcement of, creditors' rights and remedies or by
other equitable principles of general application.

         11. MISCELLANEOUS.

                  a. The Company hereby represents that all of the Company's
representations and warranties contained in the New Transaction Documents were
true and correct as of June 5, 2000 and, except as set forth on Schedule 1
hereto, are true and correct as of the date hereof (except for representations
and warranties made as of an earlier date, which shall be true and correct as of
such date).

                  b. The Company hereby represents that it has performed all
agreements and satisfied all conditions required to be performed or satisfied
prior to the date hereof by the New Transaction Documents when and as required.

                  c. The Company hereby represents that no Event of Default (as
defined in the Debentures) shall have occurred, be likely to occur or be
threatened, and no event shall have occurred which constitutes or would
constitute an Event of Default with notice or the passage of time or both, as of
the date hereof.

                  d. The Company hereby acknowledges and agrees that it has no
pending claims against any of the Investors and hereby releases, acquits and
forever discharges each of the Investors and Gleneagles from any and all
actions, causes of action, claims, demands, damages, judgments, debts, dues and
suits of every kind, nature and description whatsoever, which the Company ever
had, now has or may have against any Investor or Gleneagles on or by reason of
any matter, cause or thing whatsoever through the date hereof (immediately prior
to the execution of this letter agreement and the other New Transaction
Documents).

                  e. Each of the Investors and Gleneagles hereby acknowledges
and agrees that it has no pending claims against the Company and hereby
releases, acquits and forever
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discharges the Company from any and all actions, causes of action, claims,
demands, damages, judgments, debts, dues and suits of every kind, nature and
description whatsoever, which such Investor or Gleneagles, as the case may be,
ever had, now has or may have against the Company on or by reason of any matter,
cause or thing whatsoever through the date hereof (immediately prior to the
execution of this letter agreement and the other New Transaction Documents).

                  f. Article 6 of the Purchase Agreement (except for Section 6.5
thereof) is hereby incorporated herein by reference and shall apply to this
letter agreement with such changes as may be necessary mutatis mutandis to
conform to this letter agreement.

         By signing this letter agreement and signing, delivering and/or
accepting, as the case may be, the New Transaction Documents, each of the
Investors (severally and not jointly) and the Company agree to the terms hereof
and thereof, respectively, and each of the Investors (severally and not jointly)
agrees to promptly return a copy of this letter agreement bearing each of your
signatures and the Original Initial Warrants and Original Debentures to the
Company.

         This letter agreement may be executed in any number of counterparts,
including electronically transmitted counterparts, and each of such counterparts
shall for all purposes be deemed original, and all such counterparts shall
together constitute but one and the same instrument.

                                   Very truly yours,

                                   APPLIEDTHEORY CORPORATION


                                   By:      /s/ David A. Buckel
                                       -----------------------------------------
                                            Name:  David A. Buckel
                                            Title: Senior Vice President / CFO



                  *** Signatures continue on the next page ***
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ACCEPTED AND AGREED TO AS OF
THE DATE FIRST ABOVE WRITTEN:

INVESTORS:

HALIFAX FUND, L.P.
By: The Palladin Group, L.P., as Attorney-in-Fact


         By:  /s/ Steven W. Weiner
             ----------------------------------------
                  Name: Steven W. Weiner
                  Title:  Managing Director

PALLADIN PARTNERS I, L.P.
By: The Palladin Group, L.P., as Attorney-in-Fact


         By:  /s/ Steven W. Weiner
             ----------------------------------------
                  Name: Steven W. Weiner
                  Title:  Managing Director

PALLADIN OVERSEAS FUND LTD.
By: The Palladin Group, L.P., as Attorney-in-Fact


         By:  /s/ Steven W. Weiner
             ----------------------------------------
                  Name: Steven W. Weiner
                  Title:  Managing Director

DeAM CONVERTIBLE ARBITRAGE FUND, LTD.
By: The Palladin Group, L.P., as Attorney-in-Fact


         By:  /s/ Steven W. Weiner
             ----------------------------------------
                  Name: Steven W. Weiner
                  Title:  Managing Director

LANCER SECURITIES (CAYMAN) LTD.
By: The Palladin Group, L.P., as Attorney-in-Fact


         By:  /s/ Steven W. Weiner
             ----------------------------------------
                  Name: Steven W. Weiner
                  Title:  Managing Director
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THE GLENEAGLES FUND COMPANY
By: The Palladin Group, L.P., as Attorney-in-Fact


         By: /s/  Steven W. Weiner
             ----------------------------------------
                  Name: Steven W. Weiner
                  Title:  Managing Director


ELLIOTT ASSOCIATES, L.P.


By:      /s/ Paul E. Singer
    -------------------------------------------------
         Name: Paul E. Singer
         Title:   General Partner


ELLIOTT INTERNATIONAL, L.P.
By: Elliott International Capital Advisors Inc., as Attorney-in-Fact


By:      /s/ Paul E. Singer
    -------------------------------------------------
         Name: Paul E. Singer
         Title:   General Partner