Kevin Costello is Krembil William Rowan Hamilton Chair in Theoretical Physics at the Perimeter Institute for Theoretical Physics, Waterloo, Canada. He is an honorary member of the Royal Irish Academy and a Fellow of the Royal Society. He has won several awards, including the Berwick Prize of the London Mathematical Society (2017) and the Eisenbud Prize of the American Mathematical Society (2020). Owen Gwilliam is Assistant Professor in the Department of Mathematics and Statistics at the University of Massachusetts, Amherst.

• 1. Introduction and overview; Part I. Classical Field Theory: 2. Introduction to classical field theory; 3. Elliptic moduli problems; 4. The classical Batalin–Vilkovisky formalism; 5. The observables of a classical field theory; Part II. Quantum Field Theory: 6. Introduction to quantum field theory; 7. Effective field theories and Batalin–Vilkovisky quantization; 8. The observables of a quantum field theory; 9. Further aspects of quantum observables; 10. Operator product expansions, with examples; Part III. A Factorization Enhancement of Noether's Theorem: 11. Introduction to Noether's theorems; 12. Noether's theorem in classical field theory; 13. Noether's theorem in quantum field theory; 14. Examples of the Noether theorems; Appendix A. Background; Appendix B. Functions on spaces of sections; Appendix C. A formal Darboux lemma; References; Index.

'The central achievement of the book is in its development of a formalism that leads to classical and quantum versions of Noether's theorem, itself a familiar topic in physics, using the language of factorization algebras … Institutions employing mathematicians and theoretical physicists actively working in this area should acquire the book … Recommended.' M. C. Ogilvie, Choice Connect