Differential Algebraic Groups of Finite Dimension

Differential algebraic groups were introduced by P. Cassidy
and E. Kolchin and are, roughly speaking, groups defined by
algebraic differential equations in the same way as
algebraic groups are groups defined by algebraic equations.
The aim of the book is two-fold: 1) the provide an algebraic
geometer's introduction to differential algebraic groups and
2) to provide a structure and classification theory for the
finite dimensional ones. The main idea of the approach is to
relate this topic to the study of: a) deformations of (not
necessarily linear) algebraic groups and b) deformations of
their automorphisms. The reader is assumed to possesssome
standard knowledge of algebraic geometry but no familiarity
with Kolchin's work is necessary. The book is both a
research monograph and an introduction to a new topic and
thus will be of interest to a wide audience ranging from
researchers to graduate students.