Introduction: fundamental interactions and symmetries Relativistic invariance as an example of a global symmetry Local symmetry: spin 1: electrodynamics spin 2: gravity spin 3 / 2: supergravity Algebraic minimum Groups and their representations Algebras: algebras and Lie superalgebras associative algebras Clifford and Weyl algebras and (fermions and bosons) invariants (traces) Linear relativistic equations and representations of the Poincare group Klein-Gordon-Fock scalar field equation, quantization and unitary representations of the Poincare group Maxwell's equations, the factorization of gauge degrees of freedom, quantization Relativistic particles as representations of the Poincare group: Wigner's classification The gauge symmetries of massless fields of arbitrary spin and the Fronsdal theory of symmetric fields Geometry basics Integration of differential forms Stokes theorem and Lie derivative de Rham complex and cohomologies Connection, Yang-Mills fields Yang-Mills theory Yang-Mills action Matter fields The Higgs phenomenon Non-commutative theory Gravity and supergravity Tetrad (Cartan) formalism of gravity Einstein gravity and supergravity as gauge theories (by McDowell-Mansouri) de Sitter and anti-de Sitter spaces as vacuum solutions of gravitation theory with a cosmological term Types of tensor symmetries (Young tableaux by Howe) Free higher spin gauge fields Generalized tetrad formalism Free action Connections and σ-cohomologies The central on-mass-shell theorem examples of spins 0, 1, 2 general case Higher spin symmetries Dynamic systems as free differential algebra Examples General properties Nonlinear higher spin gauge theory The idea of the construction Klein operator and star-product Nonlinear higher spin equations Perturbative analysis Deformed Wigner oscillator and dual sp(2) algebra Prospects discussion Additional chapters Unitary representations of the anti-de Sitter algebra Unitary representations of the higher spin algebra sp(2M) invariant formalism AdS/CFT correspondence and higher spins