Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu.
The first volume considers manifolds, fiber bundles, tensor analysis, connections in bundles, and the role of Lie groups.
According to the review of James Eells, it has a "fine expositional style" and consists of a "special blend of algebraic, analytic, and geometric concepts".
An advanced text, it has a "pace geared to a [one] term graduate course".
The second volume considers submanifolds of Riemannian manifolds, the Gauss map, and the second fundamental form.