Harmonic functions of two variables: Harmonic and holomorphic functions, the Dirichlet problem on the disc, positive harmonic functions.

Subharmonic functions: Upper semicontinuous functions, subharmonic functions, the maximum principle, criteria for subharmoniciy, integrability, convexity, smoothing.

Potential theory: Potentials, polar sets, equilibrium measures, upper semicontinuous regularization, minus-infinity sets, removable singularities, the generalized Laplacian, thinness.

The Dirichlet problem: Solution of the Dirichlet problem, criteria for regularity, harmonic measure, Green's functions, the Poisson-Jensens formula.

Capacity: Capacity as a set function, computation of capacity, estimation of capacity, criteria for thinness, transfinite diameter.