This course starts from the basic linearized theory of wave phenomena: examples are chosen from electromagnetics, acoustics, elastics and other subjects and exposes the recent developments in wave propagation. The topics include : basic concepts in wave propagation; waves in layered media; scattering, transmission and reflection; waves in random media, effective medium properties, resolution analysis; applications in wave functional materials and imaging and numerical techniques in techniques in solving wave equations in heterogeneous media. Basic knowledge on eigenvalue problem, fourier transform, linear algebra, vector analysis is desired.