Basic notions, classification and main characteristics of partial differential equations. Method of characteristics for first-order PDEs. PDEs of Elliptic, parabolic and hyperbolic type. Special solutions, fundamental solutions, Green functions. The method of separation of variables. Wave propagation for scalar, vector and tensor fields. Geometric and physical properties of the waves. Diffusion equations and their analysis. Examples of the mathematical models for the propagation of acoustic, electromagnetic and elastic waves.