Non-commutative algebraic structures are at the core of recent developments of fundamental mathematics, from quantum groups (Hopf algebras) to non-commutative geometry. In this project of Research School complementary aspects are considered inside this direction : homology and cohomology, Frobenius algebras, representation theory and path algebras as well as Leavitt path algebras. Those subjects as well as their articulations will provide a first strong inside to the theory.