Character Sheaves on Reductive Lie Algebras

This paper is an introduction, in a simplified setting, to Lusztig's theory of character sheaves. It develops a notion of character sheaves on reductive Lie algebras which is more general then such notion of Lusztig, and closer to Lusztig's theory of character sheaves on groups. The development is self contained and independent of the characteristic $p$ of the ground field. The results for Lie algebras are then used to give simple and uniform proofs for some of Lusztig's results on groups.