Course: MIT OPEN COURSEWARE
Ebooks:
– What are the best differential geometry textbooks?
 Discrete Diferential Geometry of Curves and Surfaces.pdf – Tim Hofmann
 Lectures on the Differential Geometry of Curves and Surfaces.pdf Paul A. Blaga
 Lecture Notes on Differential Geometry – Mohammad Ghomi

First Steps in Differential Geometry: Riemannian, Contact, Symplectic (Undergraduate Texts in Mathematics) 2013th Edition, by
 Foundations of Differentiable manifolds and Lie groups, Frank Warner
 Calculus on Manifolds.pdf, Micheal Spivak
 Differential Geometry and Symmetric Space, Singurdur Helgason.
 Mathematical Methods of Classical Mechanics, V.I. Arnold.
 Gauge Fields, Knots, and Gravity, John C. Baez.

Applicable Differential Geometry (London Mathematical Society Lecture Note Series): M. Crampin, F. A. E. Pirani: 9780521231909: Amazon.com: Books(Differential geometry in applied mathematics and in physics)

Elementary Differential Geometry : Barrett O’Neill : Free Download & Streaming : Internet Archive

An Introduction To Differential Geometry : Eisenhart, Luther Pfahler : Free Download & Streaming : Internet Archive (with introduction to tensor calculus)

Differential Forms and Applications (Universitext) 1st ed. 1994. Corr. 2nd printing 1998 Edition, by
 Differential Geometry of Curves and Surfaces.pdf by Manredo P. do Carmo

Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in Mathematics) (v. 94), by
Web:
 nLab
 What are the differences between Differential Topology, Differential Geometry, Algebraic Topology, and Algebraic Geometry?
 Geometry Processing Algorithms – Differential Geometry
Lecture:
Math Differential Geometry
Math 352
Math 561 – The Differential Geometry of Curves and Surfaces
 Some lecture notes on Curves based on the first chapter of do Carmo’s textbook.
 Solutions to some problems from the first chapter of the do Carmo’s textbook.
 More solutions to problems from the first chapter of the do Carmo’s textbook.
 Some lecture notes on surfaces base on the second chapter of do Carmo’s textbook.
 Solutions to some problems from the second chapter of do Carmo’s textbook.
 An elementary proof that stereographic projection is conformal and another copy of this document.
 An online book on differential geometry which I like better than the Do Carmo textbook. In this book there is a careful statement of the Inverse and Implicit Function Theorems on page 3 and a proof that the three definitions of a regular surface are equivalent on page 6.
 Some lecture notes on the Gauss map based on the third chapter of do Carmo’s textbook.
 Some lecture notes on manifolds and maps that I used whenever I taught Math 761.
 http://bookzz.org/dl/498672/27b2c0

Kinematic Differential Geometry and Saddle Synthesis of Linkages
 Computational Manifolds and Applications
 Advanced Geometric Methods in Computer Science
 Basic of Algebra, Topology, and Differential Calculus.pdf
 Algebraic Geometry
 Introduction to Discrete Probability
 All books http://www.cis.upenn.edu/~jean/gbooks/home.html
Prof. Alan Macdonald
Overview of Geometric Algebra in Physics
Math.stackexchange.com
In general:
 Animov Y. Differential Geometry and Topology of Curves
 Csikós B. Differential Geometry (FREE!)
 do Carmo M.P. Differential Geometry of Curves and Surfaces – Quite popular for introductory level. Beware that ^ means cross product, and<a,> means a dot b or inner product in this text. Check out the errata list by Bjorn Poonen.
 Hicks N.J. Notes on Differential Geometry [.pdf] (FREE!)
 Kreyszig E. Differential Geometry – Neither do Carmo nor O’Neill introduce the matrix notation when they first discuss the Frenet formulae, Kreyszig does that, which is nice.
 Millman R.S. and Parker G.D. Elements of Differential Geometry
 O’Neill B. Elementary Differential Geometry
 Pressley A. Elementary Differential Geometry – Solution at the back.
 Sharipov R. Course of Differential Geometry (FREE!)
 Struik D.J. Lectures on Classical Differential Geometry
 Zaitsev D. Differential Geometry: Lecture Notes [.pdf] (FREE!)
Tensor Analysis and Manifolds:
 Abraham R., Marsden J.E. and Ratiu T. Manifolds, Tensors, Analysis and Applications (FREE!)
 Bishop R.L. and Goldberg S.I. Tensor Analysis on Manifolds
 Lebedev L.P. and Cloud M.J. Tensor Analysis
 Munkres J.R. Analysis on Manifolds
 Sharipov R. Quick Introduction to Tensor Analysis (FREE!)
 Spivak M. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus – Not as excellent as his books on single variable calculus and the five volumes differential geometry, still better than many authors.
Differential Forms:
 Arapura D. Introduction to Differential Forms [.pdf] (FREE!)
 Bachman D. A Geometric Approach to Differential Forms
 Cartan H. Differential Forms – Member of Bourbaki, get a taste of the so called French style.
 Darling R.W.R. Differential Forms and Connections
 do Carmo M.P. Differential Forms and Applications
 Flanders H. Differential Forms with Applications to the Physical Sciences
 Morita S. Geometry of Differential Forms
Others:
 An Introduction to Differential Geometry T J Willmore
 A comprehensive introduction to differential geometry Michael Spivak
 Applied Differential Geometry a Modern Introduction Tijana T Ivancevic
 A Course in Differential Geometry Thierry Aubin
 Differential Geometry and Statistics MK Murray
 A course in differential geometry and Lie groups S Kumaresan
 Applicable Differential Geometry M Crampin
 Differential Geometry Robert Geroch
 Elementary Differential Geometry AN Pressley
 Topics in Differential Geometry Peter W Michor
 Fundamentals of Differential Geometry Serge Lang
 Methods of Differential Geometry in Analytical Mechanics M de León
 Differential Geometry and Its Applications John Oprea
 Functional Differential Geometry Gerald Jay Sussman
 Applied Differential Geometry William L Burke
 Affine Differential Geometry Katsumi Nomizu
 Geometry of Differential Forms Shigeyuki Morita
 Differential and Riemannian Geometry Detlef Laugwitz
 Manifolds and Differential Geometry Jeffrey Marc Lee
 PDF Differential Geometry Gauge Theories and Gravity M Göckeler
Amazon:

Differential Forms with Applications to the Physical Sciences (Dover Books on Mathematics) Paperback – December 1, 1989 by

Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds