Finite group theory is remarkable for the simplicity of its statements -- and the difficulty of their proofs. It is essential in several branches of mathematics, notably number theory.

Finite Groups: An Introduction is an elementary textbook on finite group theory. Written by the eminent French mathematician Jean-Pierre Serre (a principal contributor to algebraic geometry, group theory, and number theory), this brand-new textbook is based upon a course given by Serre at l'École Normale Supérieure de Jeunes Filles, Paris in 1978-1979.

Each of the ten chapters is followed by a series of exercises.

Jean-Pierre Serre was awarded the Fields Medal in 1954 for his work in algebraic topology. In 2003 he was awarded the first Abel Prize by the Norwegian Academy of Science and Letters.

Serre attended the École Normale Supérieure (1945-48) and the Sorbonne (Ph.D.; 1951), both now part of the Universities of Paris. Between 1948 and 1954 he was at the National Centre for Scientific Research in Paris, and after two years at the University of Nancy he returned to Paris for a position at the Collège de France. He retired in 1994. Between 1983 and 1986 Serre served as vice president of the International Mathematical Union.

Serre was awarded the Fields Medal at the International Congress of Mathematicians in Amsterdam in 1954. Serre's mathematical contributions leading up to the Fields Medal were largely in the field of algebraic topology, but his later work ranged widely--in algebraic geometry, group theory, and especially number theory. By seeing unifying ideas, he helped to unite disparate branches of mathematics. One of the more recent phenomena to which he was a principal contributor was the application of algebraic geometry to number theory--applications now falling into a separate subclass called arithmetic geometry. He was one of the second generation of members of Nicolas Bourbaki (publishing pseudonym for a group of mathematicians) and a source of inspiration for fellow medalists Alexandre Grothendieck and Pierre Deligne.

An elegant writer of mathematics, Serre published Groupes algébriques et corps de classes (1959, Algebraic Groups and Class Fields); Corps locaux (1962, Local Fields); Lie Algebras and Lie Groups (1965); Abelian l-adic Representations and Elliptic Curves (1968); Cours d arithmétique (1970, A Course in Arithmetic); Cohomologie Galoisienne (1964, Galois Cohomology); Représentations linéaires des groupes finis (1967, Linear Representations of Finite Groups); Algèbre locale, multiplicités (1965, Local Algebra: Multiplicities); Arbres, amalgames, SL2 (1977, Trees); and, with Uwe Jannsen and Steven L. Kleiman, Motives (1994). His collected works were published in 1986. A Leroy P. Steele Prize in 1995 was awarded to Serre on the basis of A Course in Arithmetic.