Revised, updated, and translated from the 1989 Russian edition, describes the application of the method of cumulants to limit theorems on large deviations, in such a manner as to be of interest to researchers and graduate students working on probability theory, mathematical statistics, or the application of either. The method can be used to investigate large deviations for sums of both independent and dependent random variables, polynomial forms and statistics, and multiple stochastic integrals of random processes and fields. Considers only normal approximation. No subject index.