||The main purpose of this course is twofold. On the first part, the goal is to present a different formulation of Quantum Mechanics not based on operators in Hilbert space but on the Path Integral formalism and then extend this formulation from Quantum Mechanics to Quantum Field Theory. The main objects (Generating functionals and Green functions) will be introduced and computed first in a discretized form and then in a continuous form. The formalism will be applied to scalars, fermions and gauge fields. In the second part the appearance of infinities in the computation of interacting field theories will be presented and the regularization and renormalization theory will be detailed. Renormalization group theory and aspects of non-abelian gauge theories like QCD will be discussed. Finally at the end of the course some more advanced topics will be presented, namely, anomalies, hadronic tau decays and chiral perturbation theory.