Soft materials are all around us: they naturally form biological tissues and plant matter, while rubbers and gels are used as sealants, contact lenses, energy absorbers, sensors, and actuators. Most soft materials swell as they absorb fluids – in some cases this swelling is a desirable feature of the material, while in others it can be detrimental to its ability to function. It is essential to understand and model how soft materials swell, and how these swollen rubbers and gels respond to the forces they experience. This book combines perspectives from soft matter physics, nonlinear mechanics, and materials science to describe the mechanics of swelling, and serves as a reference for anyone interested in the mechanics of swelling in soft polymers, regardless of their scientific background. It provides the necessary physical and mechanical knowledge to model the behaviour of soft materials that swell by offering a comprehensive exploration of theoretical concepts, complemented by practical computational exercises.