Renormalization: regularization and UV divergencies, renormalized perturbation theory, renormalization group, Callan-Symanzik equation.

Quantum effective action: physical meaning, 1PI verte, effective potential, spontaneous symmetry breaking and Nambu-Goldstone theorem.

Abelian gauge theories: vector field and spinor field and their quantization, canonical and path-integral. QED: tree amplitudes. QED: one-loop effects, renormaliztion, beta-function and Landau pole.

Non-abelian gauge theories: continous symmetries and Lie groups. SU(N) and representations. Non-abelian lagrangian and its path-integral quantization. Ghost fields, beta-function and asymptotic freedom. BRST and unitarity. Anomalies.