This monograph is devoted to the systematic and encyclopedic presentation of the foundations of quantum field theory. It represents mathematical problems of the quantum field theory with regardto the new methods of the constructive and Euclidean field theory formed for the last thirty years of the 20th century on the basis of rigorous mathematical tools of the functional analysis the theory of operators and the theory of generalized functions. The book is useful for young scientists who desire to understand not only the formal structure of the quantum field theory but also its basic concepts and connection with classical mechanics relativistic classical field theory quantum mechanics group theory and the theory of functional integration.