  In this set of lecture notes we review the mode-coupling theory of the glass
transition from several perspectives. First, we derive mode-coupling equations
for the description of density fluctuations from microscopic considerations
with the use the Mori-Zwanzig projection operator technique. We also derive
schematic mode-coupling equations of a similar form from a field-theoretic
perspective. We review the successes and failures of mode-coupling theory, and
discuss recent advances in the applications of the theory.
