Tentative table of contents:
Introduction
Chapter 1 – How to Prove It
Chapter 2 – Logic and Set Theory
Chapter 3 – Real Numbers
Chapter 4 – Complex Numbers
Chapter 5 – Polynomials
Chapter 6 – Matrix Algebra
Chapter 7 – Derivatives
Chapter 8 – Iterated Function Systems
Chapter 9 – Analytic Functions
Chapter 10 – Möbius Transforms
Chapter 11 – Basic Number Theory
Chapter 12 – Groups
Chapter 13 – Elliptic Curves
Appendix A – Table of Notation
@JordiGH Like the topics. One word of advice is "how to prove it" as a chapter title might be troublesome, given:
https://www.cambridge.org/core/books/how-to-prove-it/6D2965D625C6836CD4A785A2C843B3DA