Elementary Differential Geometry Curves and SurfacesAsst. Prof. Martin
RaussenPDF  160 Pages  EnglishThe 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.



Lectures on Differential Geometry (PDF 221P)Wulf RossmannPDF  221 Pages  EnglishThis
note contains on the following subtopics of Differential Geometry,
Manifolds, Connections and curvature, Calculus on
manifolds and Special topics.


Lectures on Symplectic Geometry (PDF 225P)Ana Cannas
da SilvaPDF  225 Pages  EnglishThis 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 GroupsJean GallierPDF  744 Pages  EnglishThis 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 LogEuclidean Framework,
Spherical Harmonics, Statistics on Riemannian Manifolds, Distributions and the
Frobenius Theorem, The LaplaceBeltrami 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 GeometryMarkus DesernoPDF  64 Pages  EnglishThese 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 1Lars AnderssonPDF  25 Pages  EnglishThis 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 GeometryIvan
Kolar, Jan Slovak and Peter W. MichorOnline  NA Pages  EnglishThis 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 GeometryShalosh B. EkhadOnline  NA Pages  EnglishThis 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 FinslerHadwiger Theorem,
Fregier's Theorem, Fuhrmann's Theorem, Griffiths's Theorem, Incenter Exists
Theorem, Lemoine's Theorem, Ptolemy's Theorem.

Natural operations in differential geometryIvan Kolar, Jan Slovak and Peter W. MichorOnline  437 Pages  EnglishThis
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 SurfacesNigel
HitchinPDF  101 Pages  EnglishThis book covers the following topics: The topology of surfaces, Riemann
surfaces, Surfaces in R3, The hyperbolic plane.

Differentiable ManifoldsNigel
HitchinPDF  95 Pages  EnglishThis 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 spacesMatthias WeberPDF  72 Pages  EnglishThis 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 