Springer An Introduction to Manifolds

Bought this book since my university completely didn't care to teach it's mathematicians any geometry beyond Euclidean... For me this book is quite concise I worked trough the entire book during the last two weeks. It consists of a lot of small subsegments that are easily understood. Not too much unnecessary text very well structured. Cannot say how understandable it is for non mathematicians, however it for for me self studying geometry. Will see how it works now as reference manual.

When I first began reading the text, I had a difficult time understanding the concepts, but the presentation of the material really laid bare all of the esoteric topics that I hadn't encountered formally before. Loring Tu has done an excellent job of making sure even the uninitiated student can make his/her way through this text, having sprinkled a few easy exercises through the text itself to emphasize the learning and familiarity with definitions, with more difficult exercises at the end (including computations as well as topics that force a student to understand and digest the section immediately preceding the problems). He labels every problem, so a student doesn't wade through pages of text needlessly trying to discover which part of the text will be most useful, but this method allows the student to hone in on the material which is exactly pertinent to that problem. I am by far not the best and brightest student, but I have been able to read the text and given a few hours for each section, complete all exercises throughout the reading and at the end of the section. With many hints and solutions at the end of the textbook, I can be sure I'm not only learning the material, I'm learning it correctly! I would agree with some of the other reviewers that this should be a text every graduate student in mathematics should read. It is not out of the realm of possibilities for a student to read it on his/her own, and the enlightenment gained from the generalizations of multivariate calculus is really a gift to oneself, as well as to any future students the person may have, for they will be able to answer any up-and-coming student's questions with a clarity surpassing any instructor I've personally had, which would have been very helpful as a budding mathematician.

Très bon livre d’introduction ! Achat pas parfait !

Definitely the best text of manifolds for an undergraduate. Also good for a graduate student who needs an easier and more slow-paced companion to Lee's book on smooth manifolds.

Very good book