From the reviews:

"An introduction to the formalism of differential and integral calculus on smooth manifolds. … Many prospective readers of Bott and Tu will welcome this volume. … Summing Up: Recommended. Lower-division undergraduates." (D. V. Feldman, CHOICE, Vol. 45 (10), June, 2008)

"An Introduction to Manifolds is split up into eight parts, well organized, well written, and, as Tu claims, readable. … This excellent and accessible book also comes equipped with plenty of examples and exercises, whence it will serve well as both a classroom text and a source for self-study. Indeed, I propose to use it myself, given that I am one of the non-experts … ." (Michael Berg, MathDL, April, 2008)

"A book which … covers all the essential topics in differentiable manifolds theory, and sufficiently elementary so that it can be read and understood with only minimal prerequisites—all this in less than 360 pages. The book is divided into seven parts, plus four appendices. … The added value of the book lies mainly in the simplicity, the clearness and the concision of the exposition. … is certainly one of the most readable introductions to differential geometry." (Ahmad El Soufi, Mathematical Reviews, Issue 2008 k)

"The textbook under review is very well-written and self contained. … It extends the calculus of curves and surfaces to higher dimensions. The higher dimensional analogues of smooth curves and surfaces are called manifolds. … This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study." (Ion Mihai, Zentralblatt MATH, Vol. 1144, 2008)