The goal of this set of lectures is to provide an introduction to semiclassical methods and their main applications in quantum mechanics and quantum field theory. The lectures will be primarily aimed at a non-specialist audience.

The tentative plan is :

1. Euclidean path integrals: short introduction
2. Steepest descent method (one complex variable)
3. Barrier penetration effect in the semi-classical limit from instanton calculus:
   • Metastable states
   • Potentials with degenerate minima
   • Calculation of the determinant: collective coordinates
4. Barrier penetration in quantum field theory: general remarks
5. The fate of the false vacuum
6. Quantum ChromoDynamics: the strong CP problem
7. Large orders of perturbation theory