In these lecture notes we will analyze the behavior of random walk on disordered media by
means of both probabilistic and analytic methods and will study the scaling limits. We will
focus on the discrete potential theory and how the theory is effectively used in the analysis
of disordered media. The first few chapters of the notes can be used as an introduction to
discrete potential theory. Recently there has been significant progress on the theory of
random walk on disordered media such as fractals and random media. Random walk on a percolation
cluster('the ant in the labyrinth')is one of the typical examples. In 1986 H. Kesten showed
the anomalous behavior of a random walk on a percolation cluster at critical probability.
Partly motivated by this work analysis and diffusion processes on fractals have been developed
since the late eighties. As a result various new methods have been produced to estimate heat
kernels on disordered media. These developments are summarized in the notes.
