Path integrals in quantum theory. An outlook of basic concepts

M. S. Marinov

The purpose of this text is to present in a simple way the basic principles and abilities of the path integral method. The domain, where the method is useful and powerful, and its limitations, are indicated In particular, the topological aspects, phase space formulation, anticommuting variables and the application to gauge fields are considered. Semiclassical approximations and the generating functional method are discussed. The review is supposed to be an introduction to the topic.