This is a set of lecture notes given by the author at the Universities of Göttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics. Contents:IntroductionExample of a Classical and Quantum Scalar Free Field TheoryScene and Subject of the Drama. Axiom 1 and 2Subject of the DramaPrinciple of Relativity. Causality. Axiom 3, 4 and 5Irreducibility of the Field Algebra and the Scattering Theory. Axiom 6. Axiom 0Preliminaries about Physical SymmetriesCurrents and ChargesGlobal Symmetries and Supersymmetries of the S-MatrixRepresentations of the Super-Lie AlgebraThe Case of Massless ParticlesFermionic ChargesConcluding Remarks Readership: Mathematical physicists and high energy physicists. Keywords:Symmetry in Physics;Supersymmetry;Quantum Field Theory;Relativity;Spinors;SL(2,C) Group;Symplectic Space;Scalar Charges;Vector Charges;Supercharges;Central Charges;Representation of the Super Lie Algebra;Currents;S-Matrix Coleman — Mandula Theorem;Scattering Theory Coleman — Mandula Theorem