We will consider linear and nonlinear wave propagation. Equations which describe the phenomena of wave propagation are generally hyperbolic partial differential equations. In this talk ``wave“ means ``singularity of solution”. Therefore our interest is to study the singularities of solutions of hyperbolic equations. The most traditional and typical method for the singularity theory has been the “resolution of singularities”, that is to say, to lift the surfaces with singularities into higher dimensional space so that the singularities would disappear. This is a survey note of our researches from the point of view of resolution of singularities.