Contents

Abstract. We review the basic denitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel's theorem which states that each tilting triple yields an equiv-alence between derived categories. We establish its link with Rickard's theorem which characterizes derived equivalent algebras. We then examine invariants under derived equivalences. Using t-structures we compare two abelian cate-gories having equivalent derived categories. Finally, we brie y sketch a gener-alization of the tilting setup to dierential graded algebras