Lectures on Geodesics Riemannian GeometryM. BergerPDF  317 Pages  EnglishAim of this book is to give
a fairly complete treatment of the foundations of Riemannian geometry through
the tangent bundle and the geodesic flow on it. Topics covered includes: Sprays,
Linear connections, Riemannian manifolds, Geodesics, Canonical connection,
Sectional Curvature and metric structure.

Basic Riemannian GeometryF.E. BurstallPDF  29 Pages  EnglishThis note covers the following
topics: What is a manifold, Analysis on Riemannian manifolds, Geodesics and
curvature, The Bishop volume comparison theorem.

Topics in Riemannian GeometryJeff A. ViaclovskyPDF  108 Pages  EnglishThe first part of this
course note will be a review of some basic concepts in Riemannian geometry. It
then gives a fairly basic introduction to the Ricci Flow, some conformal
geometry, and look at Riemannian 4manifolds in greater depth.

Riemannian Geometry Lecture NotesH.M. KhudaverdianPDF  107 Pages  EnglishThis lecture note covers
the following topics: Riemannian manifolds, Covariant differentiaion, Parallel
transport and geodesics, Surfaces in E3 and Curvtature tensor.


Riemannian GeometryLuther Pfahler EisenhartOnline  NA Pages  EnglishA masterful sourcebook with
intriguing exercises, on the theory and application of the tensor calculus,
which is indispensable to Riemannian geometry, the Theory of Relativity, and
rfiuch of contemporary topology.

Lectures on Riemannian Geometry Complex ManifoldsStefan VandorenPDF  38 Pages  EnglishThis is an
introductory lecture note on the geometry of complex manifolds. Topics discussed
are: almost complex structures and complex structures on a
Riemannian manifold, symplectic manifolds, Kahler manifolds and CalabiYau
manifolds,hyperkahler geometries.

Semi Riemann Geometry and General RelativityShlomoSternbergPDF  251 Pages  EnglishThis book represents
course notes for a one semester course at the undergraduate level giving an
introduction to Riemannian geometry and its principal physical application,
Einstein’s theory of general relativity. The background assumed is a good
grounding in linear algebra and in advanced calculus, preferably in the language
of differential forms.

W. M. Boothby, Introduction to Differentiable Manifolds and Riemannian Geometry (djvu) 
Riemannian Geometry (Moller J.M pdf)Jesper Michael MollerPDF  59 Pages  EnglishThis
note covers the following topics: Smooth manifolds, Riemannian
manifolds, Curvature, Spacetimes, Multilinear Algebra and Noneuclidean
geometry.

A Course in Riemannian Geometry(Wilkins D.R pdf)David R.
WilkinsPDF  72 Pages  EnglishThis note covers the following topics: Smooth Manifolds ,
Tangent Spaces, Affine Connections on Smooth Manifolds, Riemannian
Manifolds, Geometry of Surfaces in R3, Geodesics in Riemannian
Manifolds, Complete Riemannian Manifolds and Jacobi Fields.

An Introduction to Riemannian GeometrySigmundur
GudmundssonPDF  111 Pages  EnglishThis note covers the following topics: Differentiable Manifolds, The
Tangent Space, The Tangent Bundle, Riemannian Manifolds, The LeviCivita
Connection, Geodesics, The Riemann Curvature Tensor, Curvature and Local
Geometry.
