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.