INTRODUCTION TO ALGEBRAIC GROUPS AND INVARIANT THEORY IVAN V. ARZHANTSEV Preface These notes originate in a series of eleven lectures and eight seminars given at the Eberhard Karls Universit Tubingen in the Spring of 2007. The material here is at based on special courses and seminars given by Professor Ernest Vinberg, Dmitri Timashev and myself at the Faculty of Mechanics and Mathematics of Moscow State University. I am grateful to everyone who attended my lectures in Tubingen for their patience and