  We use solvable two-dimensional gauge theories to illustrate the issues in
relating large N gauge theory to string theory. We also give an introduction to
recent mathematical work which allows constructing master fields for higher
dimensional large N theories. We illustrate this with a new derivation of the
Hopf equation governing the evolution of the spectral density in matrix quantum
mechanics. Based on lectures given at the 1994 Trieste Spring School on String
Theory, Gauge Theory and Quantum Gravity.
