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

Probably the best textbook on classical differential geometry of curves and surfaces.

This is a beautiful book, certainly one of my favourites. It talks about the differential geometry of curves and surfaces in real 3-space. If you want a book on manifolds, then this isn't what you're looking for (though it does say something about manifolds at the end); but it is a good book for a course just below that level, or to gain interest and motivation in preparation for a course on manifolds. Top-class exposition, a healthy number of good exercises and lots of very, very nice illustrations. Make no mistake, the book requires some comfort with so-called "advanced calculus" - the reader should be familiar with differentiation of real functions of several variables - but it's certainly a contender for "best book" for a properly prepared student. If you're buying this book to read it in your own time, i.e., it's not for some class you're attending, then you might want to check out the set of lectures on YouTube by Claudio Arezzo, posted on the ICTP channel. Just search "ICTP differential geometry" on YouTube. It's a nice set of recorded lectures based following this book. It's certainly not necessary to read and understand the book, but it will help if you have the time.

Pretty much the book that made me a geometer. Remember reading it cover-to-cover as an undergraduate, and there are few books (especially of the given depth) I can claim that of. Loved Do Carmo's writing style, approach and clarity.

There are better books available

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.

Excellent. But it is for two or three dimensional case not in generalized form. Though it is pleasure to read.