Remarkable progress has recently been made in the application of quantumtrajectories as the computational tool for solving quantum mechanical problems. This is the first book to present these developments in the broader context of the hydrodynamical formulation of quantum dynamics. In addition to a thorough discussion of the quantum trajectory equations of motion, there is considerable material that deals with phase space dynamics, adaptive moving grids, electronic energy transfer, and trajectories for stationary states. On the pedagogical side, a number of sections of this book will be accessible to students who have had an introductory quantum mechanics course. There is also considerable material for advanced researchers, and chapters in the book cover both methodology and applications. The book will be useful to students and researchers in physics, chemistry, applied math, and computational dynamics. "This excellent book covers a wide range of topics associated with Quantum Hydrodynamics. It's an excellent survey of the history, current state-of-the-field, and future research directions." Brian Kendrick,Theoretical Division, Los Alamos National Laboratory, Los Alamos,NM, USA The book is unique in that it addresses with equal expertise, computational methodology and theoretical connections at the interface between de Broglie-Bohm theory and phase space moment methods.A highly didactic text, to be recommended to graduate students and researchers in physics and chemistry. Irene Burghardt,Departement de chimie, Ecole Normale Superieure, Paris, France Wyatt shows how one can use the ideas drawn from Bohm's interpretation to develop new and efficient computational methods for both time dependent and time independent quantum mechanics.This is THE definitive text on practical Bohmian mechanics. Eric Bittner,Department of Chemistry, University of Houston, Tx, USA .