After the initial observation by John Scott Russell of a solitary wave in a canal, his insightful laboratory experiments and the subsequent theoretical work of Boussinesq, Rayleigh and Korteweg and de Vries, interest in solitary waves in fluids lapsed until the mid 1960s with the seminal paper of Zabusky and Kruskal, which described the discovery of the soliton. This was followed by the rapid development of the theory of solitons and integrable systems. At the same time came the realization that solitary waves occur naturally in many physical systems, and play a fundamental role in many circumstances. The aim of this text is to describe the role that soliton theory plays in fluids in several contexts. After an historical introduction, the book is divided into five chapters covering the basic theory of the Korteweg-de Vries equation, and the subsequent application to free-surface solitary waves in water, internal solitary waves in coastal ocean and the atmospheric boundary layer, solitary waves in rotating flows, and to planetary solitary waves with applications to the ocean and atmosphere.The final chapter examines the theory and application of envelope solitary waves and the nonlinear Schrodinger equation to water waves.