  This is an introduction to the theory of one-dimensional disordered systems
and products of random matrices, confined to the 2 by 2 case. The notion of
impurity model--- that is, a system in which the interactions are highly
localised--- links the two themes and enables their study by elementary
mathematical tools. After discussing the spectral theory of some impurity
models, we state and illustrate Furstenberg's theorem, which gives sufficient
conditions for the exponential growth of a product of independent,
identically-distributed matrices.
