Yakimiv (Steklov Institute of Mathematics) introduces Tauberian theorems and applies them to analyzing the asymptotic behavior of stochastic processes, record processes, random permutations, and infinitely divisible random variables. In particular, the book covers multidimensional extensions of Tauberian theorems due to Karamata, weakly oscillating functions, one-dimensional Tauberian theorems, Tauberian theorems due to Drozhzhinov and Zavyalov, Markov branching processes, and probabilities of large deviations in the context of the record model