This IMA Volume in Mathematics and its Applications TWIST MAPPINGS AND THEIR APPLICATIONS is based on the proceedings of a workshop which was an integral part of the 1989- 90 IMA program on "Dynamical Systems and their Applications". The workshop brought together many of the leading figures in the modern study of twist maps. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, Ken Meyer, Jiirgen Moser, Clark Robinson, George R. Sell, and Eduard...