1), M. In. Fedoryuk . Equations with fast oscillating solutions. C. 5-56. The method of the canonical operator Maslov is described, which allows to construct the asymptotics of solutions in a large one for linear equations with partial derivatives. These equations contain small parameters for older derivatives, the solutions are oscillating in nature. Applications to the problems of quantum mechanics and others. Some classes of nonlinear ordinary differential equations and partial-derivative equations with quick-oscillation solutions. are considered. 2), B. R. Weinberg . Asymptotic behavior at t->about solutions of external mixed problems for hyperbolic equations and quasiclassics. C. 57-92. Asymptotic properties of solutions of external boundary problems : short-wave and long-wave asymptotics of solutions and analytical properties of resolvent elliptic problems , asymptotics of spectral function for equations in all space , quasiclassical asymptotics of solving the scattering problem and scattering amplitudes , asymptotic behavior with an unlimited increase in the time of solving external mixed problems for hyperbolic equations . A connection is established between the departure of wave fronts and the decrease in local energy . 3), B. M. Babich . Multivariate ICD method or radiation method. Its analogies and generalizations. C. 93-134. The article describes the main asymptotic methods of the theory of wave diffraction. The radiation method, field structure near caustics, Gaussian beams, method of summation of Gaussian beams, waves of whisper gallery type. are considered. 4), B. F. Lazutkin . Quasiclassical asymptotics of proper functions. C. 135-174. The article contains a statement of the quasiclassical method for obtaining asymptotics of the discrete spectrum of a multidimensional differential operator . The basis for constructions is the Kolmogorov invariant set in the phase space of the corresponding classical dynamical system. The number of eigenvalues approximated by asymptotics is estimated by the measure of the Liouville Kolmogorov set divided by the volume . A history of the issue and an overview of the literature. 5), A. M. Ilyin . Border layer. C. 175-214. Methods for solving certain classes of boundary problems for partial differential equations containing a small parameter. are presented. The main focus is on the method of harmonizing asymptotic decompositions, which is also called - the method of splicing, the method of gluing, crosslinking, and t. p. Methods are illustrated by specific examples of edge tasks. 6), H. C. Bakhvalov, G. P. Panasenko, A. L. Staras. Method of averaging for partial-derivative equations and its application. C. 215-240. Asymptotic and numerical-asymptotic methods of solving equations in partial derivatives describing fields and processes are considered; in heterogeneous environments, weakly nonlinear problems are investigated.