Pseudo-reductive groups arise naturally in the study of general
smooth linear algebraic groups over non-perfect fields and have
many important applications. This monograph provides a
comprehensive treatment of the theory of pseudo-reductive groups
and gives their classification in a usable form. In this second
edition there is new material on relative root systems and Tits
systems for general smooth affine groups, including the extension
to quasi-reductive groups of famous simplicity results of Tits in
the semisimple case. Chapter 9 has been completely rewritten to
describe and classify pseudo-split absolutely pseudo-simple groups
with a non-reduced root system over arbitrary fields of
characteristic 2 via the useful new notion of 'minimal type' for
pseudo-reductive groups. Researchers and graduate students working
in related areas, such as algebraic geometry, algebraic group
theory, or number theory will value this book, as it develops tools
likely to be used in tackling other problems.
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