Read
**Fill in Gaps**:
Lang - Basic Mathematics
Apostol - Calculus
**Royal Road To Differential Geometry and Physics**:
Lawvere - Sets for Mathematics Shilov - Linear Algebra (and)
Lev Landau - courses in physics Volume 1+2 (then) Bishop - Tensor Analysis (or)\*
Sternberg - Differential Geometry (then)\*\*
Isu Vaisman - Cohomology and Differential Forms
**Backbone**:
Arnold - Ordinary Differential Equations
Kaplansky - Set Theory and Metric Spaces (and)
Edmund Landau - Foundations of Analysis (then) Rudin - Principles of Mathematical Analysis
Bradley, Bryson, Terrilla - Topology: A Categorical Approach
Ahlfors - Complex Analysis Olver - Applications of Lie Groups to Differential Equations
Aluffi - Algebra Chapter 0 (or) \*
Lang - Algebra\*\*
\* = easier
\*\* = direct
**Good General Videos**:
https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic
notes:
https://drive.google.com/file/d/1nchF1fRGSY3R3rP1QmjUg7fe28tAS428/view