I think that your basis is good to start studying Chiral Perturbation Theory. Let me give you some references.
All standard textbooks cover the basics of Chiral Perturbation theory (CPT), but I suggest you to start from Effective Field Theories(EFTs). Indeed, the CPT is the most famous example of EFT and it's a good starting point to understand all the physics behind EFTs.
The review by Georgi is a very good one, you can find it here, read it.
Then, regarding Chiral Perturbation Theory, I suggest you the following references
Matthew D. Schwartz, Quantum Field Theory and the Standard Model
- Chapter 22.3 : You can find a short introduction to the theory of mesons
- Chapter 28 : It treats spontaneous symmetry breaking and then it discuss shortly the Chiral Lagrangian.
Introduction to Chiral Perturbation Theory, Stefan Scherer, 0210398 hep-ph
- This is more a review you can find on arXiv. It covers a lot of interesting topic. Try to read it.
S.Weinberg, The Quantum Theory of Fields: Volume 2, Modern Applications
- Chapert 19: this is absolutely the best treatement about spontanous symmetry breaking and theory of mesons. I suggest you to read it when you will have a bit of familiarity with EFTs and CPT from the resources I gave you before.