Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)

I wish that this book was available when I took a senior level differential geometry course in college. Very good diagrams, careful attention to detail My only suggestion would be to have larger dimensions for the book so that the fonts are larger and easier to read. Here and there, I have to use a magnifier to be able to clearly see superscripts and subscripts

Very good intro to differential geometry. The prerequisites are: a basic course in linear algebra, calculus, and an intro course in real analysis. Anything more than this (such as a course on differential equations) would be helpful but isn't necessary. With the said prerequisites, you should be able to follow most, if not all, the proofs. Hard cover books obviously tend to be more durable and longer lasting than paperback ones. However, I'm actually pleased with this book. The paper quality and printing is good and the binding is standard quality for a paperback book. If you treat the book reasonably, then the book should definitely last you long enough to read the book inside and out. There are still typos (ranging from grammatical errors to typos such as h_{uu} instead of h_{vu} or a missing "<") but there aren't a lot of them, so confusion due to typos should be minimal. Overall, the math content of the book is perfect for a first introduction to differential geometry. The quality of the physical paperback book is also pretty good, considering you can buy it for a good price of $20. If you have $20 and are trying to learn differential geometry for the very first time, I'd recommend buying this book.

I find every book written by Do Carmo to offer a very good exposition also with good problems to properly learn the subject.

very nice and clear book, but be aware that it does not talk about metrics etc it uses a much simpler notation to explain common ideas of diff geo instead, without even introducing metric tensor, wedge product etc..

I brought this book for self learnig. it is indeed a very good material. Another nice thing about it is that it is so popular, you can find tones of supplimental material online, including solution to ex. and dicussion on forum. Its more likely your doubts have been already asked, answered and posted online. Some downside of this book, it is old. Some topic can be presented better

Docarmo seems to be used in a lot of differential geometry classes, and this second edition cleans up errors in the earlier edition (and adds a few) and expands on some of the material and problems. The book is clearly for classroom use and less for self-study. A lot (really, a lot) of the material "happens" in the problems, of which there are many. That's all well and good if you're in a class, but not if you want to learn on your own. The book lacks a bit of balance. Some things get covered in more detail than others, and it's not necessarily based on importance. But on the other hand, I found the explanations to be pretty lucid and easy enough to follow. And the big plus is that, at least by the outrageous standard of math texts, the book is inexpensive. Supplement this with on-line material (there's a lot, and some excellent video lectures) and/or another book. I picked up a copy of J.J. Stoker's book on Differential Geometry (a little expensive for a used edition but worth it) and found it to be more rigorous and complete, and good for reference and filling in some gaps. I'm probably swimming against the tide but I give Docarmo 4 stars. I don't think the book rises to the 5 star level.

A classic. Read a scanned PDF version (which is low quality) in 2014 summer. It's nice to have a hard copy and read it again. DoCarmo did a really good job to explain things. You won't regret to have this one.

so much better than Kreyszig's from Dover. This book is clear and goes in depth on the analysis of functions. I like this becuase it helps me review continuous mappings, parametrized surfaces and curves, vector functions, and Real Analysis in general. This book doesnt really use any Tensors (good because I haven't studied Tensors yet). It does use Christoffel Symbols later in the book.

Needless to say, one of the best books in CDG in world. For Sure!!!

El libro del prof Do Carmo es el mejor texto para un curso inicial de Geometria Diferencial! Excelentes imagenes y un esfuerzo notable de compaginar la intuición geométrica con el formalismo matemático

Considera los temas más importantes y esenciales de la geometría diferencial, excelente obra del matemático brasileño Manfredo Do Carmo, con una exposición clara del tema y buenos ejercicios. No solo debería leerse por los profesionales de la matemática, sino también por los aficionados entusiastas, pues la geometría diferencial cuenta con muchos de los resultados más interesantes de la matemática, y por supuesto, yo considero que este libro es la mejor opción, una reimpresión barata, buena y bonita de Dover

Very authoritative text covers a lot material and interesting example problems. Not an easy read for me: it sometimes skips over development which the author thinks is "straightforward". Only some problems are provided with solutions. I am benefitting greatly and this is a book you would want on your shelf for reference should this subject be of interest.

Der nicht ganz leichte Inhalt wird im gut gegliederten Buch so dargestellt, dass das Lesen nicht zu einem frustrienden Graus wird. Anhänge ermöglichen eine rasche Auffrischung einiger Grundlagen. Die Aufgaben variieren im Schwierigkeitsgrad, so dass wohl jede Leserin und jeder Leser passenden Übungsstoff findet. Hilfreich ist der Teil, der Hinweise und Lösungen zu den Aufgaben anbietet. Besonders erfreuten mich die kommentierten Hinweise auf weitere Literatur.