I. Equations with Rapidly Oscillating Solutions.- II. Asymptotic Expansion as t?3 ? of the Solutions of Exterior Boundary Value Problems for Hyperbolic Equations and Quasiclassical Approximations.- III. The Higher-Dimensional WKB Method or Ray Method. Its Analogues and Generalizations.- IV. Semiclassical Asymptotics of Eigenfunctions.- V. The Boundary Layer.- VI. The Averaging Method for Partial Differential Equations (Homogenization) and Its Applications.- Author Index.