This work represents a treatment of both classical and modern problems of pulse propagation. The authors provide a physical insight in the intriguing problem of pulse propagation in non-equilibrium media (unstable or admitting attenuation). A refined analysis of the acoustic-gravity waves generation in a compressible stratified fluid is also presented. The solution describes sophisticated wave pictures near the front of the perturbation where previously known methods fail. Finally a detailed account of a relatively new field of investigation related to continuous spectrum waves in shear flows is given.