Feynman categories and representation theory

We give a presentation of Feynman categories from representation--theoretical viewpoint. Feynman are special type monoidal and their representations functors. They can be viewed as far reaching generalization groups, algebras modules. Taking new algebraic approach, we provide more examples details for several key constructions. This leads to applications results. The text is intended self--contained basis crossover elevated constructions results in the fields representation theory categories, whose so include number theory, geometry, topology physics.