This monograph developed from a course given at the Courant Institute in the spring of 1976. At that time a preliminary set of notes was prepared for the class by M. Lewandowsky, who also contributed Chapter 4 and made numerous helpful suggestions. My purpose at the time was to provide a brief complement to the relevant portions of Lighthill's book, Mathematical Biofluiddynamics, as well as a guide to the papers contained in the symposium proceedings Swimming and Flying in Nature, edited by Wu, et al, and to incorporate background and supplementary material as needed. The present book has been changed only by the addition of Chapter 12 on interactions and a number of revisions and corrections.

Although, as a result of these origins, this monograph falls far short of a definitive treatise, I hope that this glimpse of a fascinating and rapidly evolving body of research will be useful to students of fluid mechanics seeking a compact introduction to biological modeling. Those familiar with the aerodynamics of fixed-wing aircraft or the hydrodynamics of ships, to take two examples from many, are well aware that in these applications the theory is concerned with design as well as analysis. The products of our technology are both the subjects and the results of our mathematical modeling. In “natural” swimming and flying the situation is no longer the same. Nature has already provided the answers.