About the Book: This book introduces beginning graduate students to frequently used techniques in modern global geometry, assuming a solid background in multivariable calculus, linear algebra, and point-set topology. It emphasizes learning through examples and combines classical differential geometry with a global and analytical perspective. Topics include algebraic-topological methods on smooth manifolds (Poincaré duality, Thom isomorphism, intersection theory, characteristic classes, Gauss–Bonnet theorem) and analytic techniques (elliptic equations, elliptic (L^p) and Hölder estimates, Fredholm and spectral theory, Hodge theory, Dirac-type operators). The second edition adds numerous examples, exercises, and a new chapter on classical integral geometry.