Differential Topology

"This book is written for mathematics students who have had one year of analysis and one semester of linear algebra. Included in the analysis background should be familiarity with basic topological concepts in Euclidean space: openness, connectedness, compactness, etc. We borrow two theorems from analysis which some readers may not have studied: the inverse function theorem, which is used throughout the text; and the change of variable formula for multiple integration, which is needed only for Chapter 4"--Page xiii.