Quadratic Lagrangians in quantum gravitation and the problem of renormalizability

The problem of renormalization in quantum gravitation is reviewed with attention given to the following topics: the back reaction of the quantized field, one-loop divergencies, field theories of nonlocalized action, consistent supergravity, and the theory of dual models and strings. The development of first-order formalism for the study of gravitational fields with nonminimal action is discussed.