In present book are represented obtained by authors results of investigations of various unsteady problems of waves propagation in different media. In Introduction there are described obtained solutions of problems for three dimensional linear and nonlinear waves, including investigations of diffraction nonlinear problems, caustics, nonlinear quasi-monochromatic waves, narrow nonlinear gaussian beams, various unsteady mixed boundary value problems of elasticity, solved by Wiener-Hopf technique and derivation of solution in Smirnov-Sobolev form, exact 3D method of determination of frequencies of vibrations of magneto-elastic and piezo-electric plates and shells by derivation of transcendent equations and their numerical solution, as well as, in solution of problems of investigation of probabilities and prognosis for stochastic processes in various branches of science.