Group theory. Discrete groups, elementary examples and properties. Lie groups, Lie algebras, generators. Their fundamental properties. Group representations. O(3), SU(2), SU(3), Lorentz groups and their applications. Complex variables: algebra, Cauchy-Riemann conditions, harmonic functions. Complex variables integrals: Cauchy theorem, Cauchy formula. Laurent series. Residues calculus: isolated singular points, poles, calculation of integrals using residues, other applications. Branches, singularities on the path of integration. Conformal mapping and its applications. Green functions. Their connection to complex variables calculus. Advanced, retarded, causal GF, application in physics. Integral equations.