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Quantum field theory (QFT) is one of the great achievements of physics, of profound interest to mathematicians, yet standard texts often assume a physicist's background or adopt an abstract mathematical perspective. This thoroughly updated edition bridges that gap. While maintaining a rigorous approach wherever possible, it focuses on explaining what physicists do and why, using precise mathematical language. Written for readers with a background in mathematics but no prior knowledge of physics, and largely self-contained, it presents both essential physical ideas and the necessary mathematical tools in detail. This revised edition has been improved throughout, with many clarifications to the text and the inclusion of solutions to selected exercises to enhance its use for self-study. It will appeal to mathematicians seeking an accessible path into QFT and to physics students wanting greater rigor.