Actions and Invariants of Algebraic Groups

This text provides an introduction to geometric invariant theory, linking the basic theory of affine algebraic groups to Mumford's more sophisticated theory. It is intended as a self-contained treatment that will provide a basis for studying specialized texts and papers on geometric invariant theory. The authors begin with the theory of affine algebraic groups, providing necessary prerequisites in commutative algebra, algebraic geometry, and the theory of semi-simple Lie algebras over fields of characteristic zero. They have included exercises at the end of each chapter to confer expertise when dealing with fundamental concepts.