Lattice quantum field theory of the Dirac and gauge fields : selected topics SU(N) compact lie groups SU(N) Kac Moody algebra SU(N) path integrals SU(3) character functions Fermion calculus Non Abelian lattice gauge field Abelian lattice gauge field in d=3 Lattice gauge field mass renormalization Gauge field block spin renormalization Lattice gauge field Hamiltonian Dirac lattice path integral Dirac Hamiltonian Lattice gauge theory Hamiltonian. Quantum Chromodynamics is the theory of strong interactions: a quantum field theory of colored gluons (Yang Mills gauge fields) coupled to quarks (Dirac fermion fields). Lattice gauge theory is defined by discretizing spacetime into a four dimensional lattice and entails defining gauge fields and Dirac fermions on a lattice. The applications of lattice gauge theory are vast from the study of high energy theory and phenomenology to the numerical studies of quantum fields. Lattice Quantum Field Theory of the Dirac and Gauge Fields: Selected Topics examines the mathematical foundations of lattice gauge theory from first principles. It is indispensable for the study of Dirac and lattice gauge fields and lays the foundation for more advanced and specialized studies