Abstract
In this thesis we prove that the Tamarkin-Tsygan calculus of a finite dimensional associative algebra over a field is a derived invariant. In other words, the mainresult of this work goes as follows: a derived equivalence between two finite dimensional associative algebras over a field induces an isomorphism between Hochschild homology and Hochschild cohomology that respects simultaneously the cup product, the cap product, the Gerstenhaber bracket and the Connes differential.