Lanthanide
The lanthanoid (according to IUPAC terminology) (previously lanthanide) series comprises the 15 elements with atomic numbers 57 through 71, from lanthanum to lutetium.    All lanthanoids are f-block elements, corresponding to the filling of the 4f electron shell, except for lutetium which is a d-block lanthanoid. The lanthanoid series (Ln) is named after lanthanum.

# Terminology
The trivial name "rare earths" is sometimes used to describe all the lanthanoids together with scandium and yttrium. The term "rare earths" arises from the minerals from which they were isolated, which were uncommon oxide-type minerals. The use of this name is deprecated by IUPAC, as they are neither rare in abundance nor "earths" (an obsolete term for water-insoluble strongly basic oxides of electropositive metals incapable of being smelted into metal using late 18th century technology). These elements are in fact fairly abundant in nature, although rare as compared to the "common" earths such as lime or magnesia. Cerium is the 26th most abundant element in the Earth's crust, neodymium is more abundant than gold and even thulium (the least common naturally-occurring lanthanoids) is more abundant than iodine.  Despite their abundance, even the technical term "lanthanoids" reflects a sense of elusiveness on the part of these elements, as it comes from the Greek  (lanthanein), "to lie hidden."
IUPAC currently recommends the name lanthanoid rather than lanthanide, as the suffix "-ide" generally indicates negative ions whereas the suffix "-oid" indicates similarity to one of the members of the containing family of elements. In the older literature, the name "lanthanon" was often used.  There are alternative arrangements of the periodic table that exclude lanthanum or lutetium from appearing together with the other lanthanides.

# Chemistry
Lanthanoids are chemically similar to each other. Useful comparison can also be made with the actinoids, where the 5f shell is partially filled.  The lanthanoids are typically placed below the main body of the periodic table in the manner of a footnote. The full-width version of the periodic table shows the position of the lanthanoids more clearly.
The ionic radii of the lanthanoids decrease through the period  the so-called lanthanoid contraction.  Except for cerium (III and IV) and europium (III and II), the lanthanides occur as trivalent cations in nature.  As a consequence, their geochemical behaviors are a regular function of ionic radius and, therefore, atomic number.  This property results in variations in the abundances of lanthanides that  trace natural materials through physical and chemical processes.  In addition, two of the lanthanides have radioactive isotopes with long half-lives (147Sm and 176Lu) that  date minerals and rocks from Earth, the Moon and meteorites. The lanthanide contraction is responsible for the great geochemical divide that splits the lanthanides into light and heavy-lanthanide enriched minerals, the latter being almost inevitably associated with and dominated by yttrium.  This divide is reflected in the first two "rare earths" that were discovered: yttria (1794) and ceria (1803). The divide is driven by the decrease in coordination number as the ionic radius shrinks, and is dramatically illustrated by the two anhydrous phosphate minerals, monazite (monoclinic) and xenotime (tetragonal).  The geochemical divide has put more of the light lanthanides in the earths crust, but more of the heavies in the earth's mantle.  The result is that although large rich orebodies are found that are enriched in the light lanthanides, correspondingly large orebodies for the heavies are few. The lanthanides obey the Oddo-Harkins rule, which states that odd-numbered elements are less abundant than their even-numbered neighbors.
Most lanthanides are widely used in lasers. These elements deflect UV and Infrared electromagnetic radiation and are commonly used in the production of sunglass lenses.
Due to their specific electronic configurations, lanthanide atoms tend to lose three electrons, usually 5d1 and 6s2, to attain their most stable oxidation state as trivalent ions.
The lanthanide trications, feature a Xe core electronic configuration with the addition of n 4f electrons, with n varying from 0  to 14 . This 4fn sub-shell lies inside the ion, shielded by the 5s2 and 5p6 closed sub-shells. Thus, lanthanide trications are sometimes referred to as triple-positively charged noble gases.
The contracted nature of the 4f orbitals, coupled with their small overlap with the ligand atom orbitals, attaches a predominantly ionic character to lanthanide-ligand atom bonds in complexes. Thus, the mainly electrostatic interactions between the lanthanide trication and the atoms of the ligands result in irregular geometric arrangements and a handful of high coordination numbers. Indeed, this triple-positively charged closed shell inert gas electron density characteristic is the foundation of the lanthanide Sparkle Model, used in the computational chemistry of lanthanide complexes.
Several properties, such as ionization energies, optical properties, magnetic moments and geometries of complexes, etc, serve as proof that the 4f orbitals are indeed wholly shielded from ligand effects.
Lanthanides entering the human body due to exposure to various industrial processes can affect metabolic processes. Trivalent lanthanide ions, especially La3+ and Gd3+, can interfere with calcium channels in human and animal cells. Lanthanides can also alter or even inhibit the action of various enzymes. Lanthanide ions found in neurons can regulate synaptic transmition, as well as block some receptors (for example, glutamate receptors).

# Properties
All lanthanides closely resemble lanthanum.  They are electropositive trivalent metals.  They are shiny and silvery-white, and tarnish easily when exposed to air.  Many  make steel.  They react violently with most nonmetals. They are relatively soft but their hardness increases with their atomic number.  Lanthanides burn in air.  They have high melting and boiling points.

# Mnemonics
To remember the sequence of the lanthanide elements, various mnemonic phrases have been used. This is the most common one:
Ladies Can't Put Nickels Properly into Slot-machines. Every Girl Tries Daily, However, Every Time You Look.