Dr. Bruce Ikenaga's notes on algebra

https://sites.millersville.edu/bikenaga/abstract-algebra-1/abstract-algebra-1-notes.html

1. For transition to advanced mathematics:

Mathematical Proofs: A Transition to Advanced Mathematics by Albert D. Polimeni, Gary Chartrand, and Ping Zhang

This book outlines proof techniques very methodically. It works well for students who haven't been introduced to mathematical proofs before or want to learn writing proofs in a systematic way.

2. For junior/senior level undergraduate real analysis course

I find Dr. Vern Paulsen's notes for Math 4331 and 4332 courses at the University of Houston extremely helpful. If you'd like to get a hold of those notes, please let me know.

3. For first-time Measure Theory learner:

Introduction to Measure Theory by G. de Barra

de Barra introduces measure theory from a more familiar, concrete setting (the real numbers) before jumping into a more abstract setup. It is a more gentle introduction to measure theory than Folland's book Real Analysis: Modern Techniques and Their Application

1. For undergraduate level topology:

Introduction to Topology: Pure and Applied by Franzosa and Collins

Basic Topology by M.A.Amstrong

2. For graduate level topology

Topology by James Munkres

1. Books

Introduction to Ergodic Theory by Peter Walters

Dynamical Systems: Stability, Symbolic Dynamics, and Chaos by Clark Robinson

Nonlinear Dynamics and Chaos by Steven H. Strogatz

2. Dr. Vaughn Climenhaga maintains some notes on lectures from the past Houston Dynamical Systems Summer School. You can find them on: https://www.math.uh.edu/~climenha/math.html