  We give a pedagogical introduction into the functional renormalization group
treatment of disordered systems. After a review of its phenomenology, we show
why in the context of disordered systems a functional renormalization group
treatment is necessary, contrary to pure systems, where renormalization of a
single coupling constant is sufficient. This leads to a disorder distribution,
which after a finite renormalization becomes non-analytic, thus overcoming the
predictions of the seemingly exact dimensional reduction. We discuss, how the
non-analyticity can be measured in a simulation or experiment. We then
construct a renormalizable field theory beyond leading order. We discuss an
elastic manifold embedded in N dimensions, and give the exact solution for N to
infinity. This is compared to predictions of the Gaussian replica variational
ansatz, using replica symmetry breaking. We further consider random field
magnets, and supersymmetry. We finally discuss depinning, both isotropic and
anisotropic, and universal scaling function.
