"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literatureappear for the first time in a text."

Mathematical Reviews (Review of the Second Edition)

An affordable softcover edition of a classic text Introduces the theory of algebraic groups over an algebraically closed field Second Edition thoroughly revised and expanded, extending the theory over arbitrary fields which are not necessarily algebraically closed Excellent exercises, bibliography and index May be used as a textbook in graduate and advanced undergraduate courses on Algebra, Modern Algebra, and Linear Algebra Includes supplementary material: sn.pub/extras

Inhalt
Some Algebraic Geometry.- Linear Algebraic Groups, First Properties.- Commutative Algebraic Groups.- Derivations, Differentials, Lie Algebras.- Topological Properties of Morphisms, Applications.- Parabolic Subgroups, Borel Subgroups, Solvable Groups.- Weyl Group, Roots, Root Datum.- Reductive Groups.- The Isomorphism Theorem.- The Existence Theorem.- More Algebraic Geometry.- F-groups: General Results.- F-tori.- Solvable F-groups.- Freductive Groups.- Reductive F-Groups.- Classification.