Introduction Notation and Conventions Introduction Notation and Conventions Part 1 Classical and Parabolic Potential Theory Chapter I Introduction to the Mathematical Background of Classical Potential Theory 1.The Context of Green's Identity 2.Function Averages 3.Harmonic Functions 4.Maximum-Minimum Theorem for Harmonic Functions 5.The Fundamental Kernel for RN and Its Potentials 6.Gauss Integral Theorem 7.The Smoothness of Potentials; The Poisson Equation 8.Harmonic Measure and the Riesz Decomposition Part 2 Probabilistic Countrepart of Part 1 Part 3 Appendixes