The basic definition. What is a random walk in a random environment? How do the issues of recurrence and transience, the law of large numbers and the central limit theorem etc. differ from the case of classical random walks? Explicit calculations are presented in special examples when the space dimension is 1.

How is the question of large deviations affected by the random environment?
The difference between quenched and annealed versions. The use of the sub-additive ergodic theorem in the quenched case.

Hopf-Cole transformation and the reduction of large deviations to the study of homogenization of a random Hamilton-Jacobi equation with a quadratic Hamiltonian and a small parameter. More general equations with convex Hamiltonians and a variational formula. The time dependent case.