Gravity-capillary flows, in which the effects of pipe flow, gravity flow, and surface tension combine to produce a singular flow pattern, are utilised in many practical applications. The effect of surface tension on gravity-capillary flows continues to be a fertile field of research in applied mathematics and engineering. Concentrating on applications arising from fluid dynamics, Professor Vanden-Broeck's volume draws from his own results, collected from years of experience in the subject, and places this knowledge within the context of recent developments. Whilst careful numerical techniques are implemented to solve the basic equations, an emphasis is placed upon the reader developing a deep understanding of the structure of the resulting solutions. Surface flows are treated for cases where there may, or may not, exist intersections between the flow and rigid bodies; other examples include free bubbles rising in a fluid and solitary waves.