This volume aims to acknowledge J. E. Marsden's influence as a teacher, propagator of new ideas, and mentor of young talent. It presents both survey articles and research articles in the fields that represent the main themes of his work, including elesticity and analysis, fluid mechanics, dynamical systems theory, geometric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread throughout is the use of geometric methods that serve to unify diverse disciplines and bring a wide variety of scientists and mathematicians together in a way that enhances dialogue and encourages cooperation. This book may serve as a guide to rapidly evolving areas as well as a resource both for students who want to work in one of these fields and practitioners who seek a broader view.