"e;Methods of the Classical Theory of Elastodynamics"e; dealsnot only with classical methods as developed in the pastdecades, but presents also very recent approaches. Applications and solutions to specific problems serve toillustrate the theoretical presentation. Keywords: Smirnov-Sobolev method with further developments;integral transforms; Wiener-Hopf technique; mixedboundary-value problems; time-dependent boundaries;solutions for unisotropic media (Willis method); 3-ddynamical problems for mixed boundary conditions.