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This section contains free e-books and guides on Differential Geometry, some of the resources in this section can be viewed online and some of them can be downloaded.

Differential Geometry Books
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Elementary Differential Geometry Curves and Surfaces

PDF | 160 Pages | English
The purpose of this course note is the study of curves and surfaces , and those are in general, curved. The book mainly focus on geometric aspects of methods borrowed from linear algebra; proofs will only be included for those properties that are important for the future development.

 
Differential Geometry Of Three Dimensions

Online | 280 Pages | English
This book describes the fundamentals of metric differential geometry of curves and surfaces.

 
Projective differential geometry old and new from Schwarzian derivative to cohomology of diffeomorphism groups

PDF | 281 Pages | English
This book is addressed to the reader who wishes to cover a greater distance in a short time and arrive at the front line of contemporary research. This book can serve as a basis for graduate topics courses. Exercises play a prominent role while historical and cultural comments relate the subject to a broader mathematical context.

 
Lectures on Differential Geometry (PDF 221P)

PDF | 221 Pages | English
This note contains on the following subtopics of Differential Geometry, Manifolds, Connections and curvature, Calculus on manifolds and Special topics.

 
Lecture Notes on Differential Geometry

Online | NA Pages | English
This is a useful note for Differential Geometry. This note covers Curves, Surfaces and Manifolds

 
Lectures on Symplectic Geometry (PDF 225P)

PDF | 225 Pages | English
This note contains on the following subtopics of Symplectic Geometry, Symplectic Manifolds, Symplectomorphisms, Local Forms, Contact Manifolds, Compatible Almost Complex Structures, Kahler Manifolds, Hamiltonian Mechanics, Moment Maps, Symplectic Reduction, Moment Maps Revisited and Symplectic Toric Manifolds.

 
Notes on Differential Geometry and Lie Groups

PDF | 744 Pages | English
This note covers the following topics: Matrix Exponential; Some Matrix Lie Groups, Manifolds and Lie Groups, The Lorentz Groups, Vector Fields, Integral Curves, Flows, Partitions of Unity, Orientability, Covering Maps, The Log-Euclidean Framework, Spherical Harmonics, Statistics on Riemannian Manifolds, Distributions and the Frobenius Theorem, The Laplace-Beltrami Operator and Harmonic Forms, Bundles, Metrics on Bundles, Homogeneous Spaces, Cli ord Algebras, Cli ord Groups, Pin and Spin and Tensor Algebras.

 
Notes on Differential Geometry

PDF | 64 Pages | English
These notes are an attempt to summarize some of the key mathematical aspects of differential geometry,as they apply in particular to the geometry of surfaces in R3. Covered topics are: Some fundamentals of the theory of surfaces, Some important parameterizations of surfaces, Variation of a surface, Vesicles, Geodesics, parallel transport and covariant differentiation.

 
Geometry and linear algebra
Notes on Differential Geometry, Lars Andersson 1

PDF | 25 Pages | English
This note covers the following topics: Linear Algebra, Differentiability, integration, Cotangent Space, Tangent and Cotangent bundles, Vector fields and 1 forms, Multilinear Algebra, Tensor fields, Flows and vectorfields, Metrics.

 
Lecture Notes in Differential Geometry (PS)
Natural Operations in Differential Geometry

Online | NA Pages | English
This book is a monographical work on natural bundles and natural operators in differential geometry and this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry.

 
Plane Geometry

Online | NA Pages | English
This book explains about following theorems in Plane Geometry: Brianchon's Theorem, Carnot's Theorem, Centroid Exists Theorem, Ceva's Theorem, Clifford's Theorem, Desargues's Theorem, Euler Line Exists Theorem, Feuerbach's Theorem, The Finsler-Hadwiger Theorem, Fregier's Theorem, Fuhrmann's Theorem, Griffiths's Theorem, Incenter Exists Theorem, Lemoine's Theorem, Ptolemy's Theorem.

 
Natural operations in differential geometry

Online | 437 Pages | English
This book covers the following topics: Manifolds And Lie Groups, Differential Forms, Bundles And Connections, Jets And Natural Bundles, Finite Order Theorems, Methods For Finding Natural Operators, Product Preserving Functors, Prolongation Of Vector Fields And Connections, General Theory Of Lie Derivatives.

 
Projective Geometry
Geometry of Surfaces

PDF | 101 Pages | English
This book covers the following topics: The topology of surfaces, Riemann surfaces, Surfaces in R3, The hyperbolic plane.

 
Differentiable Manifolds

PDF | 95 Pages | English
This book covers the following topics: Manifolds, Tangent vectors and cotangent vectors, Vector fields, Tensor products, Differential forms, Integration of forms, The degree of a smooth map, Riemannian metrics.

 
Minimal surfaces in Euclidean spaces

PDF | 72 Pages | English
This book covers the following topics: Basic Differential Geometry Of Surfaces, The Weierstrass Representation, Minimal surfaces on Punctured Spheres, The Scherk Surfaces, Minimal Surfaces Defined On Punctured Tori, Higher Genus Minimal Surfaces.

 
Differential Geometry Lecture Notes
Differential Geometry A First Course in Curves and Surfaces
Differential Geometry and Physics
Course of differential geometry
Complex Analytic and Differential Geometry
Topics in Differential Geometry
Functional Differential Geometry
Differential Geometry Csikos B.
Quick Introduction to Tensor Analysis
Introduction to Differential Forms
Complex Manifolds and Hermitian Differential Geometry
Differential Geometry Reconstructed A Unified Systematic Framework
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