>>14344283I recommend starting with Ferdinand de Saussure to set the stage for the historical development of the field. Basic Linguistic Theory by Dixon is a three volume monster but it is probably the best description of a modern structuralist framework for linguistics. You'll also want to understand generativism and how it compares with structuralism. You can go directly to Chomsky if you like, OP's book is probably written from that perspective.
I don't have a good book for phonetics in English but I recommend downloading an open source program called Praat and using it to analyze recordings as you're learning it. If you're learned math at university level you're going to recognize that most of that subject revolves around the Fourier transform.
For phonology I again don't have a good book in English but I would generally recommend an overview of dialects in your native language or a language you're learning as a good place to start.
For semantics Riemer's "Introductory Semantics" should work. Any other introductory semantics text will do. It's fairly easy to read. Something on formal semantics might also be fun.