In concluding this book we give a brief commentary regarding the main results forth in the foregoing. In order to make the book accessible not only to specialists, but also to students and engineers, we give in Chapter 1 a complete account of definitions and notations and present a number of relevant topics from other branches of mathematics. The detailed outline of mathematical models leading to partial differential equations is available in many textbooks and monographs on equations of mathematical physics. In particular, we refer the reader to Courant and Hilbert (1953, 1962), Godunov (1971), Morse and Feshbach (1953), Tikhonov and Samarskii (1963). Current exposition follows the best legacies of the past: my first book with my dear teacher - the late Academ. Tikhonov "Equations of Mathematical Physics", throughout which the reader can find thorough, advancedundergraduate to graduate level treatments of problems leading to partial differential equations: hyperbolic, parabolic, elliptic equations; wave propagations in space, heat conduction in space, special functions, etc. with emphasis on the mathematical formulation of problems, rigorous solutions, physical interpretation of the results obtained.