Course Description: Harmonic and caloric measures are fascinating objects at the cross roads of GMT, PDE, and probability. In this course, we will explain the basic connection between harmonic and caloric measures, Laplace’s equation, the heat equation, and Brownian motion. We will show two methods to construct the measures, give examples of the measures on elementary domains, and illustrate how to use the maximum principle and the fundamental solutions of the PDEs to estimate the Hausdorff dimension of the measures on arbitrary domains from below.