Asymptotic estimates are of key significance to mathematical analysis and its applications, assisting investigators whose calculations become too complicated or impossible. This monograph, a major contribution to the literature upon its original publication, retains its value by working out specific examples that illustrate general methods with clarity and precision. The three-chapter treatment introduces principal methods of obtaining asymptotic estimates, discusses basic material from the theory of entire functions of finite order, and applies the first chapter's methods to the functions of the second chapter. M. A. Evgrafov presents the basic material of the theory of entire functions in the closest possible connection with asymptotic estimates in order to obtain material for examples and to enable readers to efficiently master the theory. For advanced undergraduates and graduate students in mathematics. AUTHOR: Russian-Soviet mathematician M. A. Evgravov (1926 97) served on the faculty of the Moscow Physical-Technical Institute. Dover also publishes his Analytic Functions.