The first study in the scientific literature on the space-time beam method (PVLM), which makes it possible to interpret numerous wave processes from a single point of view. The space-time asymptotics of the solutions of the wave equation, Maxwell equations, etc. are considered. Much attention is paid to PVLM applications and specific physical tasks, in particular the propagation of tsunami waves over uneven bottoms, etc. The book is designed for specialists in the field of radiophysics, geophysics, acoustics and mathematical physics.