Here are some recommended books on classical field theory:
"Classical Field Theory" by Davison E. Soper: This book provides a comprehensive introduction to classical field theory, covering topics such as Lagrangian and Hamiltonian formulations, symmetries and conservation laws, and electromagnetic fields. It includes exercises and examples to enhance understanding.
"Classical Field Theory: Electromagnetism and Gravitation" by Francis E. Low: This book presents a clear and concise introduction to classical field theory, focusing on electromagnetism and gravitation. It covers topics such as Maxwell's equations, energy-momentum tensors, and the principle of least action.
"Classical Electrodynamics" by John David Jackson: Although primarily focused on classical electrodynamics, this book covers the foundations of classical field theory. It offers a rigorous treatment of the subject, discussing topics such as electromagnetic waves, radiation, and relativistic covariance.
"Field Theory: A Modern Primer" by Pierre Ramond: This book provides an introduction to classical field theory from a modern perspective, emphasizing the symmetry and geometric aspects of the subject. It covers topics such as Lagrangian and Hamiltonian formalisms, gauge theories, and the quantization of fields.
"Quantum Field Theory in a Nutshell" by A. Zee: While this book primarily focuses on quantum field theory, it includes an introductory section that covers classical field theory. It provides a clear and accessible treatment of the subject, discussing topics such as classical Lagrangian and Hamiltonian mechanics, symmetries, and Noether's theorem.
These books should provide a solid foundation in classical field theory, catering to different levels of mathematical rigor and depth of coverage. Depending on your background and interests, you can choose the one that suits you best.