This text is an elementary introduction to differential geometry. Although it was written for a graduate-level audience, the only requisite is a solid back- ground in calculus, linear algebra, and basic point-set topology. The first chapter covers the fundamentals of differentiable manifolds that are the bread and butter of differential geometry. All the usual topics are cov- ered, culminating in Stokes' theorem together with some applications. The stu- dents' first contact with the subject can be overwhelming because of the wealth of abstract definitions involved, so examples have been...

Riemannian manifolds, particularly those with positive or nonnegative curvature, are constructed from only a handful by means of metric fibrations or deformations thereof. This text documents some of these constructions, many of which have only appeared in journal form. The emphasis is less on the fibration itself and more on how to use it to either construct or understand a metric with curvature of fixed sign on a given space.

This text is an elementary introduction to differential geometry. Although it was written for a graduate-level audience, the only requisite is a solid back- ground in calculus, linear algebra, and basic point-set topology. The first chapter covers the fundamentals of differentiable manifolds that are the bread and butter of differential geometry. All the usual topics are cov- ered, culminating in Stokes' theorem together with some applications. The stu- dents' first contact with the subject can be overwhelming because of the wealth of abstract definitions involved, so examples have been...