The book provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.

A reader-friendly volume which will be very useful to those wishing to know more about the structure of algebraic groups ... contains both a straightforward guide to the simpler ideas in the subject, and also a fascinating glimpse into some of the more abstruse areas which are the subject of current investigation.

--Bulletin of the LMS

Table of Contents

• Review of semisimple groups
• Basic facts about classes and centralizers
• Centralizers of semisimple elements
• The adjoint quotient
• Regular elements
• Parabolic subgroups and unipotent classes
• The unipotent variety and the flag variety
• Nilpotent orbits and unipotent classes
• Finite groups of Lie type
• Springer's Weyl group representations
• Complements
• References
• Index