The following table of contents, as well as the above title,  changes weekly. The book should be completed by the end of 1999 and will appear in pdf format on a CD. Additional chapters will
include Poisson's Equation, Mutual Energy, Dirichlet Forms, Harmonic Spaces, and Diffusion Processes.
 

0  Preliminaries

0.1    Notation
0.2    Useful Theorems
 

1.1    Introduction
1.2    Green's Theorem
1.3    Fundamental Harmonic Function
1.4    The Mean Value Property
1.5    Poisson Integral Formula
1.6    Gauss' Averaging Principle
1.7    The Dirichlet Problem for a Ball
1.8    Kelvin Transformation
1.9    Neumann Problem for a Disk
1.10  Neumann Problem for a Ball
1.11  Spherical Harmonics
 

2.1    Introduction
2.2    Sequences of Harmonic Functions
2.3    Superharmonic Functions
2.4    Properties of Superharmonic Functions
2.5    Approximation of Superharmonic Functions
2.6    Perron-Wiener Method
2.7    Harmonic Measure
 

3.1    Introduction
3.2    Green Functions
3.3    Symmetry of the Green Function
3.4    Green Potentials
3.5    Riesz Decomposition
3.6    Continuity Properties of Potentials

4.1    Introduction
4.2    Superharmonic Extensions
4.3    Reduction of Superharmonic Functions
4.4    Capacity
4.5    Boundary Behavior of the Green Function
 

5.1    Introduction
5.2    Exterior Dirichlet Problem
5.3    Dirichlet Problem for Unbounded Regions
5.4    Boundary Behavior

6.1    Poisson's Equation
6.2    The Reflection Principle