Many systematic introductions to the foundations of the edifice of Differential Geometry appeared in the sixties, and they are useful references even today. Some of them are:
- Lang, Introduction to Differentiable Manifolds, 1962;
- Helgason, Differential Geometry and Symmetric Spaces, 1962;
- Kobayashi, Nomizu, Foundations of Differential Geometry, 1st Vol 1963, 2nd Vol 1969;
- Sternberg, Lectures on Differential Geometry, 1964;
- Bishop, Crittenden, Geometry of Manifolds, 1964;
From Abraham's review of Lang's textbook:
From modest beginnings in the eighteenth century, differential calculus has had a continuous increase of power and scope, culminating recently with the global theory of differential manifolds and mappings. This theory, basic to modern differential topology and geometry as well as classical physics, emerges from two decades of semi-secret existence with the publication of this definitive Introduction.
