The emergence of observing systems such as acoustically-trackedfloats in the deep ocean, and surface drifters navigating bysatellite has seen renewed interest in Lagrangian fluid dynamics.Starting from the foundations of elementary kinematics and assumingsome familiarity of Eulerian fluid dynamics, this book reviews theclassical and new exact solutions of the Lagrangian framework, andthen addresses the general solvability of the resulting generalequations of motion. A unified account of turbulent diffusion anddispersion is offered, with applications among others to planktonpatchiness in the ocean. Written at graduate level, the bookprovides the first detailed and comprehensive analyticaldevelopment of the Lagrangian formulation of fluid dynamics, ofinterest not only to applied mathematicians but alsooceanographers, meteorologists, mechanical engineers,astrophysicists and indeed all investigators of the dynamics offluids.