The topics of this project are finite groups and their modular representations, Morita and Rickard equivalences between blocks of group algebras, characters, saturated fusion systems, group cohomology, block cohomology or more generally cohomology of fusion systems and Hochschild cohomology of group algebras and their blocks. The research in this field is very intense on international level and has multiple ramifications and applications. We intend to combine classical with modern methods, but especially we will evidentiate methods of homological algebra which can apply in this context. We propose to involve in these subjects young researchers and to present these topics and the obtained results on national and international level. The main directions of investigation (of theoretical and computational nature) are: the study of the invariants (and their relations) of blocks algebras viewed as finite dimensional algebras and of the invariants which comes from the fact that these blocks are factors of finite group algebras; equivalences of Brauer categories (isomorphisms, equalities of fusion systems); Morita and Rickard equivalences, the computation and the study of block cohomology, the study of BV-algebras, BD-algebras operators associated to Hochschild cohomology, the study of the first Hochschild cohomology of blocks of group algebras (Linckelmann's conjecture).