This second edition explores wave propagation in heterogeneous materials, focusing on electromagnetic and elastic waves in matrix composites and polycrystals under time-harmonic fields. Employing self-consistent methods, the book evaluates phase velocities and attenuation factors, comparing theoretical predictions with experimental data and simulations. Reflecting the shift in analytical practices due to advanced computational tools like Mathematica and MATLAB, this edition emphasizes detailed calculation algorithms over complex final formulas. Notable revisions include expanded coverage of scalar wave homogenization methods, streamlined chapters on wave propagation, and an appendix featuring specialized tensor computation codes.