Instantons in gauge theories: solutions of Euclidean equations of motion. Sad- dle points of path integrals. Instantons as self-dual connections. The k = 1 solution.
ADHM construction. The moduli space of self-dual connections. Fermions in the instantons background.
Supersymmetric theories. Supersymmetry in the instanton moduli space. N = 1 supersymmetric gauge theories. The Affleck-Dine-Seiberg prepotential.
N= 2 supersymmetric gauge theories. The idea of localisation. The prepotential. Multi-instanton calculus via localization..
