Direct methods in the calculus of variations:

• semicontinuity and convexity,

• coerciveness and reflexivity,

• relaxation and minimizing sequences,

• properties of integral functionals.

Gamma-convergence:

• definition and elementary properties,

• convergence of minima and of minimizers,

• sequential characterization of Gamma-limits,

• Gamma-convergence in metric spaces and Yosida approximation,

• Gamma-convergence of quadratic functionals.

G-convergence:

• abstract definition,

• connection with Gamma-convergence,

• convergence of eigenvalues and eigenvectors.

The localization method for Gamma-convergence:

• increasing set functions and their regularizations,

• measures, fundamental estimate for subadditivity,

• integral representation of Gamma-limits,

• compactness of elliptic operators with respect to G-convergence,

• homogenization problems for convex integral functionals,

• homogenization of elliptic operators.