This book is dedicated to basic physical principles of the propagation of acoustic and elastic waves. It consists of two volumes. The first volume includes 8 chapters and extended Appendices explaining mathematical aspects of discussed problems. The first chapter is devoted to Newton's laws, which, along with Hooke's law, govern the behavior of acoustic and elastic waves. Basic concepts of mechanics are used in deriving equations which describe wave phenomena. The second and third chapters deal with free and forced vibrations as well as wave propagation in one dimension along the system of elementary masses and springs which emulates the simplest elastic medium.In addition, shear waves propagation along a finite and infinite string are discussed.In chapter 4 the system of equations describing compressional waves is derived.The concepts of the density of the energy carried by waves, the energy flux, and the Poynting vector are introduced. Chapter 5 is dedicated to propagation ofspherical, cylindrical, and plane waves in homogeneous media, both in time andfrequency domains. Chapter 6 deals with interference and diffraction. Thetreatment is based on Helmholtz and Kirchhoff formulae. The detailed discussion of Fresnel's and Huygens's principles is presented. In Chapter 7 the effects of interference of waves with close wave numbers and frequencies are considered. Concepts such as the wave group, the group velocity, andthe stationary phase important for understanding propagation of dispersive waves are introduced. The final chapter of the first volume is devoted to the principles of geometrical acoustics in inhomogeneous media.