This is a list of books which you should study in order. That being said, of course, each person is different and you might skip this and that. In any case, this is what should have worked for me back when I was a student.
You need to understand how to apply the least action principle for simple finite systems:
- Mechanics, Course of Theoretical Physics Vol. 1, 3rd Edition – L.D. Landau, E.M. Lifshitz
ISBN-10: 0750628960, ISBN-13: 978-0750628969
You need to understand how to apply the least action principle for classical fields:
- The Classical Theory of Fields, Course of Theoretical Physics Vol. 2, 4th Revised Edition – L.D. Landau, E.M. Lifshitsz
ISBN-10: 0750627689, ISBN-13: 978-0750627689
You need to understand quantum mechanics:
- Quantum Mechanics: A Modern Development, 2nd Edition – L. E. Ballentine
ISBN-10: 9814578576, ISBN-13: 978-9814578578 - Lectures on Quantum Mechanics, 2nd Edition – S. Weinberg
ISBN-10: 9781107111660, ISBN-13: 978-1107111660
You need to understand Lie groups and Lie algebras because every symmetry is expressed in terms of a Lie group:
- Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, 2nd Edition – B. C. Hall
ISBN-10: 3319134663, ISBN-13: 978-3319134666
- The Quantum Theory of Fields, Vol. 1 – S. Weinberg
ISBN-10: 0521670535, ISBN-13: 978-0521670531 - The Conceptual Framework of Quantum Field Theory, A. Duncan
ISBN-10: 0199573263, ISBN-13: 978-0199573264