Path Integral: path integral formulation of quantum mechanics; Path Integral Quantization: scalar field, spinor field, gauge field, correlation functions, 2-point functions, 4-point functions, Feynman rules, generating functional. Functional derivatives, QED, functional determinants; Renormalization of φ4 Theory: power counting of ultraviolet divergences, one-loop structure if φ4 theory, dimensional regularization, Pauli-Villar regularization; Renormalization of QED: one-loop structure of QED, renormalization beyond the leading order; Spontaneous Symmetry Breaking: renormalization and symmetry, explicit and spontaneous symmetry breaking, Nambu-Goldstone theorem, example; Effective Action: idea of the effective action, effective action for the linear sigma model, effective action as the generating function; Wilsonian Renormalization: Wilson’s approach to renormalization, renormalization condition, the Callan-Symanzik equation, beta and gamma function in renormalization group; Evolution of Parameters: solution of Callan-Symanzik equation, application in QED, concept of running coupling constant, evolution of parameters and operators; Statistical Mechanics and Field Theory: quantum field theory and statistical mechanics, partition function in statistical mechanics, the critical phenomena; Critical Exponents: theory of critical exponents, spin correlation function, exponents of thermodynamic functions, values of the critical exponents, critical behavior in 4-dimensions; Perturbation Theory Anomaly: definition, axial anomaly, toy example: axial current in 2-dimensions, vacuum polarization operator, current operator, fermion number non-conservation, axial current in 4-dimensions, triangle diagrams, spontaneous breaking of chiral symmetry, anomalies of chiral current, chiral gauge theories, anomalous breaking of scale invariance.