Reserving my five stars for the absolute best for me. This book comes close to five. It maybe as good as it gets with 4.5.
This book is truly a gem! It is very special and eloquently written! Among many introducotry books for upper undergraduates, I highly recommend this book. It is approachable and sticks to the essentials. You can go far with this book into beginning mathematical physics or gravitation. Don't let the notation fool you to what it is saying with them! It is subtle and elegant.
The notation is special in the sense it is standard and that it uses simply slightly subtle concepts. Like the different notation between a scalar and a vector, it may look the same to the uninitiated but it isn't. I love the emphasis of what one much know as a reader after he gives you the concept. It is slightly better than the Schaum's Outline series for concciseness and that is saying a lot! Better because of its simplicity and eloquence.
I recommend this book after reading Elie Cartan's Riemannian Geometry on Orthogonal Frames. Harry Lass's book is a kinder and gentler experience than the standard and sophistication of Cartan's work.
If you want to get somewhere with as much time as you have, make the most of it with this book. It is elementary and it will get you the fundamentals you need to learn mathematical physics or pure mathematics.
Many books' heart is not about the title. The heart of this book is more vector analysis with one chapter on tensor notation; while, the rest is about mathematical physics or applied math such as electromagneticism and gravitation. With the special bonus: Einstein's field equations in the very end to end the book. A gem with a sparkle too!
In conclusion, this makes an excellent self-study for a beginner in pure mathematics or the undergraduate student that has already some exposure to vector analysis notation. A very refreshing joy to do and also to read book. You may read at first reading to get an overview; but you miss out on the meat, if you don't do the exercises. The explanations and expository material is great without the exercises to do also. They can only clarify and expound on it!
Lots of patience and love here put into a book for beginners and for self-study people. You may treasure this book for years to come!