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Classical solutions play an important role in quantum field theory, high energy physics, and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, which have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology, and related fields, this book brings the reader up to the level of current research in the field. Its first half discusses the most important classes of solitons: kinks, vortices, and magnetic monopoles, and their cosmological and observational constraints. The second half is devoted to Euclidean solutions, with particular emphasis on Yang-Mills instantons and on bounce solutions. This title is also available as open access on Cambridge Core.