This textbook serves as an introduction to modern differential geometry at a level accessible
to advanced undergraduate and master's students. It places special emphasis on motivation and
understanding while developing a solid intuition for the more abstract concepts. In contrast
to graduate level references the text relies on a minimal set of prerequisites: a solid
grounding in linear algebra and multivariable calculus and ideally a course on ordinary
differential equations. Manifolds are introduced intrinsically in terms of coordinate patches
glued by transition functions. The theory is presented as a natural continuation of
multivariable calculus the role of point-set topology is kept to a minimum. Questions
sprinkled throughout the text engage students in active learning and encourage classroom
participation. Answers to these questions are provided at the end of the book thus making it
ideal for independent study. Material is further reinforced with homework problems ranging from
straightforward to challenging. The book contains more material than can be covered in a single
semester and detailed suggestions for instructors are provided in the Preface.
