Marcel Berger, Riemannian Geometry During the Second Half of the Twentieth Century, (2000) University Lecture Series vol. 17, American Mathematical Society, Rhode Island, ISBN 0-8218-2052-4. (Provides a historical review and survey, including hundreds of references.)
Jurgen Jost, Riemannian Geometry and Geometric Analysis, (2002) Springer-Verlag, Berlin ISBN 3-540-4267-2 (Provides a formal introduction, written at the grad-student level.)
Peter Peterson, Riemannian Geometry, (1998) Springer-Verlag, Berlin ISBN 0-387-98212-4. (Provides an introduction, presented at an undergrad level.)