Title: Restriction between cohomology algebras of blocks of finite groups Autor: C.C. Todea; Abstract: Let $k$ be an algebraically closed field of characteristic $p$ and $G$ be a finite group. Let $N$ be a normal subgroup of $G$ and $c$ be a $G$-stable block of $kN$. We shall discuss the cohomology algebra of the block $c$, defined by M.~ Linckelmann and, in this case a generalized block cohomology which can be defined using some generalized Brauer pairs, denoted $(c,G)$-Brauer pairs, which were are introduced by R.~Kessar and R.~ Stancu. We also analyze the restriction map between these two cohomology algebras associated to the block $c$ through transfer maps between the Hochschild cohomology algebras of $kGc$ and of the block $c$. Status: to appear "Algebras and Representation Theory"