This book covers recent developments in the wave theory with applications to physical oceanography, plasma, optics, acoustics, astrophysics, solids, condensed matter, including Bose-Einstein condensation, and other fields. Separate chapters written by leading experts in physics and mathematics represent new information on surface and internal waves, including rogue waves, tsunami waves, solitons, waves in solid waveguides. Some authors will present materials on wave interactions, complex dynamics, chaos, stochasticity, and fractional dynamics, as well as on pattern formation and their dynamics. We also plan to include chapters containing experimental results on wave dynamics in laboratory sets up and in the field, as well as some chapters on rigorous mathematical methods in the wave theory. The most recent books on overlapping topics were published more than 10 years ago; therefore, it is reasonable to review the progress in this field.