This is a developing area of modern probability theory, which has applications in many areas. This volume is devoted to the systematic study of results on large deviations in situations where Cramer's condition on the finiteness of exponential moments may not be satisfied

This text includes coverage of asymptotic expansions taking into account the cases when the number of summands comparable with the sum is less than or equal to two and asymptotic expansions of the probabilities of large deviations and non-uniform estimates of remainders in CLT.