Mathematics

Algebra

• Benedict Gross Abstract Algebra video lectures from the Harvard, course Mathematics 122
• Michael Artin - Algebra
• Serge Lang - Algebra
• Nathan Jacobson - Basic Algebra
• Paolo Aluffi - Algebra: Chapter 0

Analysis

• Stephen Abott - Understanding Analysis
• Xavier GOURDON - Les maths en tête, Analyse
• Walter Rudin - Principles of mathematical analysis

Topology

• MAT327 - Introduction to Topology notes from University of Toronto
• James Munkers - Topology

Differential Geometry

• Kristopher Tapp - Differential Geometry of Curves and Surfaces
• ICTP Diploma - Differential Geometry - Claudio Arezzo on youtube
• These lecture notes of Zuoqin Wang are great
• Loring W. Tu - An Introduction to Manifolds (2011, Springer)
• Serge Lang - Introduction to Differentiable Manifolds, Second Edition

Probability

• Achim Klenke - Probability Theory: A Comprehensive Course
• Durrett - Probability Theory and Examples

Logic and Foundations

• Joseph Mileti - Modern Mathematical Logic
• Category Theory. Mathematics PhD course, 2022-23., great lecture notes

mix of all

• Xavier BUFF, Emmanuel HALBERSTADT François MOULIN, Monique RAMIS Jacques SAULOY - Mathematiques Tout-en-un pour la Licence (reviewed by Alain Connes)

Other great resources on internet

• Qualifying Exam - Anya Michaelsen, Great page, very very useful even not for doing qualifying exam!
• math discord booklist
• ariana1729 book list