This book is devoted to the analysis of old (classical) and new (non-Lie) symmetries of the fundamental equations of quantum mechanics and classical field theory, and to the classification and algebraic-theoretical deduction of equations of motion of arbitrary spin particles in both Poincaré invariant approach. The authors present detailed information about the representations of the Galilei and Poincaré groups and their possible generalizations, and expound a new approach for investigating symmetries of partial differential equations; this leads to finding previously unknown algebras and groups of invariance of the Dirac, Maxwell and other equations.