Differential Geometry

# Textbooks

## Introductory

• Fortney - A Visual Introduction to Differential Forms and Calculus on Manifolds
  Cute and normal undergrad-tier introduction with a lot of graphical hand-holding
  
  
• Tapp - Differential Geometry of Curves and Surfaces
  Introduction to calculus on manifolds; Spivak but with pictures
  
  
• Bachman - A Geometric Approach to Differential Forms
  Gentle introduction without going too deep into analysis

## Formal

• Shifrin - Multivariable Mathematics
  Multivariable calculus, linear algebra and differential forms packed into one textbook
  
  
• Spivak - Calculus on Manifolds
  Mathematically heavy but accessible introduction after Calculus IV

## Weird and Applied

• Lugo - Differential Geometry in Physics
  {???}
  
  
• Burke - Div Grad Curl are Dead
  {???} Idiosyncratic, esoteric, borderline masochistic read, like RMS but for mathematical physics

# Notes and Handouts

• Dona Arapura - Supplement
  Informal introduction starting from meaningless symbols and building up meaning

# Lecture Videos

• XylyXylyX - What is a manifold?
  {???}
  
  
• David Metzler - Introduction to Differential Forms
  {???}
  
  
• Shifrin - Multivariable Calculus and Linear Algebra
  Same content as his book, but in ✨video✨