Description: An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.
Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.Review Quotes: "For students at the graduate level ... I cannot think of a more accessible introduction to this subject. The book is obviously written with the student reader in mind. ... [T]his book would be an excellent choice for an early-graduate course in algebraic geometry and algebraic groups, or (including the last chapter) for a more advanced graduate course on topics in finite groups." --MAA Reviews