Computation Complexity books for a mathematician

I recently attented to some computational complexity talks (or complexity theory, I am not sure which is the correct name) and I fell in love with it. I would like to find some books, online courses... in general resources of any kind to self-study this (securely) wonderfull subject.

My backgrund is pure mathematics with emphasys in discrete mathematics (graph theorey, crypto, coding thoery, combinatorics...), with no background in computer science. I am not sure if the last one is mandatory.

Michael Sipser's text book Introduction to the Theory of
Computation
is a classic introduction to computation theory, and gives an
introduction to complexity theory in the end.

I don't know how to answer the question better than just providing the
table of contents of the book.

PART 1: AUTOMATA AND LANGUAGES.
1. Regular Languages.
2. Context-Free Languages.

PART 2: COMPUTABILITY THEORY.
3. The Church-Turing Thesis.
4. Decidability.
5. Reducibility.
6. Advanced Topics in Computability Theory.

PART 3: COMPLEXITY THEORY.
7. Time Complexity.
8. Space Complexity.
9. Intractability.
10. Advanced Topics in Complexity Theory.

StackExchange Computer Science Q#127365, answer score: 11