  This is an elementary introduction to a method for studying harmonic maps
into symmetric spaces, and in particular for studying constant mean curvature
(CMC) surfaces, that was developed by J. Dorfmeister, F. Pedit and H. Wu. There
already exist a number of other introductions to this method, but all of them
require a higher degree of mathematical sophistication from the reader than is
needed here. The authors' goal was to create an exposition that would be
readily accessible to a beginning graduate student, and even to a highly
motivated undergraduate student. Constant mean curvature surfaces in Euclidean
3-space, and also spherical 3-space and hyperbolic 3-space, are described,
along with the Lax pair equations that determine their frames. The simplest
examples, including Delaunay surfaces and Smyth surfaces, are described in
detail.
