Actions and invariants of algebraic groups (Second edition.)

This book provides an introduction to geometric invariant theory by providing the reader with the tools needed to read the research in this field. Beginning with commutative algebra and algebraic geometry, the book develops the necessary background of affine algebra over an algebraically closed field K and then moves toward the eventual application of invariant theory, Lie algebras, and modern invariant theory. Two new chapters cover observable actions of affine algebraic groups and observable subgroups of affine monoids.