This advanced level textbook for applied mathematicians, engineers, and seismologists delves into the ubiquitous natural processes of wave propagation and scattering. In applying equations of elasticity—model equations and Fourier and Laplace transforms, Harris (theoretical and applied mechanics, U. of Illinois at Urbana- Champaign) posits that understanding plane wave interactions underlies fathoming more complex interactions, and that waves are best understood in the linear approximation where they are governed primarily by their propagation environments. Topics covered include reflection, refraction, propagation of interfacial waves, integral representations, radiation and refraction, and propagation in closed and open waveguides. Chapters include problems to work.