In this monograph, the author develops theoretically on the base of a lot of various own experiments including some unique ones a concept of dual-energetic martensite (CODEM): macromonodomain and polydomain; which insures the comprehensive understanding of the shape memory phenomena.All well-known phenomena in SMA¿s such as martensite stabilization, degradation of memory properties in work cycles of memory actuators, return points memory, two-way memory effect are simply explained in the context of this concept. The dissipation of elastic energy during the martensitic transformations takes place due to the coalescence of martensite polydomains and the annihilation of the phase boundaries with building of internal domain boundaries and increase martensite free energy.The experimental methods particularly suitable for investigating SMA are also described and analyzed in detail. Finally, five own German and international patents and utility models as example of practical applications of SMA¿s in different areas of technology are presented.This monograph is particularly suitable for students, scientists, and engineers in this field.