1. Gaussian integrals 2. Path integral in quantum mechanics 3. Partition function and spectrum 4. Classical and quantum statistical physics 5. Path integrals and quantization 6. Path integral and holomorphic formalism 7. Path integrals: fermions 8. Barrier penetration: semi-classical approximation 9. Quantum evolution and scattering matrix 10. Path integrals in phase space QUANTUM MECHANICS: MINIMAL BACKGROUND A1 Hilbert space and operators A2 Quantum evolution, symmetries and density matrix A3 Position and momentum. Scrodinger equation