Kinks and domain walls are the simplest kind of solitons and are invaluable for testing various ideas and for learning about non-perturbative aspects of field theories. They are the subject of research in essentially every branch of physics, ranging from condensed matter to cosmology. This book, first published in 2006, is an introduction to kinks and domain walls and their principal classical and quantum properties. The book examines classical solitons, building from examples in elementary systems to more complicated settings. The formation of solitons in phase transitions, their dynamics and their cosmological consequences are further discussed. The volume concludes with an explicit description of a few laboratory systems containing solitons. This text will be of interest to both graduate students and academic researchers in theoretical physics, particle physics, cosmology and condensed matter physics. This book has been reissued as an Open Access publication on Cambridge Core.