Curvature of Space and Time, with an Introduction to Geometric Analysis is an undergraduate-level textbook for mathematics and physics students on differential geometry, focusing on applications to general relativity.

Its goals include both providing a shortened path for students to reach an understanding of Einstein's mathematics, and promoting curvature as a central way of describing shape and geometry.

[1][2] Chapter 2 includes vector fields, gradients, divergence,[2] directional derivatives, tensor calculus,[1] Lie brackets,[3] Green's identities, the maximum principle, and the Levi-Civita connection.

[1] Reviewer Hans-Bert Rademacher calls this a "remarkable book", with "excellent motivations and insights", but suggests it as a supplement to standard texts and courses rather than as the main basis for teaching this material.

[2] And although finding fault with a few details, reviewer Justin Corvino suggests that, with faculty guidance over these rough spots, the book would be suitable both for independent study or an advanced topics course, and "required reading" for students enthusiastic about learning the mathematics behind Einstein's theories.