Many fascinating and technologically relevant features of quantum transport rely on phase-coherent propagation in the presence of disorder. In this course, we will introduce the basic tools needed to describe disorder-induced localization phenomena and describe modern developments within this field.

First, from basic models describing the physics of quantum transport and Anderson localization in one-dimensional random systems, we go over to the predictions of scaling theory and cover an impressive number of recent experimental results in d=1,2,3 dimensions.

Then, adopting a more microscopic approach to quantum transport, we introduce Green functions and sketch the relevant diagrammatic expansions.

Finally, we describe the workings of the self-consistent localization theory and compare its predictions to results of state-of-the art numerical and laboratory experiments.