1 Overview 2 Proof of Chevalley's Theorem 3 Applications and developments 4 Complete homogeneous varieties 5 Anti-affine groups 6 Homogeneous vector bundles 7 Homogeneous principal bundles Bibliography Index

This book originates from a series of 10 lectures given by Professor Michel Brion at the Chennai Mathematical Institute during January 2011. It presents a theorem due to Chevalley on the structure of connected algebraic groups, over algebraically closed fields, as the starting point of various other structure results developed in the recent past