"When all has been said, one important fact emerges: this book is a valuable compendium of results that every expert in hydrodynamics, gas dynamics, or dynamical meteorology will want to keep by … [their]side and refer to frequently." — Bulletin of the American Mathematical Society This unique graduate-level monograph offers a heavily mathematical treatment of the vorticity of fluids. The subject's wealth of applications extends to many areas of physics and engineering, and the book will also appeal to mathematically oriented historians of science. Starting with consideration of geometrical and kinematical preliminaries, the text advances to examinations of vorticity, the vorticity field, vorticity measures, and vorticity averages. Subsequent chapters explore Bernoullian theorems, convection and diffusion of vorticity, and circulation-preserving motions.