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 tĂȘte, 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