This is a text which, while considered an introduction and perhaps a bit dated nowadays, requires some of the closest attention I have ever had to pay to a mathematical work. If I may call this book a mathematical gold mine, I must also say that in parts the digging is arduous and rewarding and the rock can be of high density. The section in chapter 2, on derivatives of composite functions (essentially Bell Polynomials, after the famous Eric Temple Bell), is an example.
This is at least my third pass through the book and this time I decided not to slough over some of the details on these polynomials. I found myself bewildered for a couple of days, as the author gives no assistance to the reader--no doubt to help the reader develop some of that mathematical maturity mentioned in the preface--and found gold thereby. Statements made apparently as an aside, such as "completely determined..." had not been paid adequate attention by me. Also, it was not pointed out by the author that certain constants evaluated in the examples were found by setting the variable to zero, and so on. This is all left to the reader to dig out. In a span of two or three pages in this section there are hours of profitable work left to the reader. This is not a complaint, but rather a statement of the level of audience addressed by this book. It is not a text for readers who require hand-holding. However, anyone who is prepared to dig will experience the "joy of finding things out", if I may humbly steal a favored phrase of the late, great Richard P. Feynman.