First Steps in Differential Geometry : Riemannian, Contact, Symplectic (Undergraduate Texts in Mathematics)

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as \"the study of structures on the tangent space