This book doesn't hold back with details and complete proofs.
It's a very good read, although you need to be confident with knowledge on differential geometry and multi-variable calculus and have a good understanding of mappings from one space to another, especially in 3 dimensions.
One improvement with this book would be to have solutions to the exercises, I've had to write all of the solutions myself so my students have guidance beyond the book.
This text is certainly an improvement on Do carmo's 'Differential Geometry of Curves and Surfaces' which is good but a very long winded read for students.