>>9
Well, it's not an analysis book. Proof theoretical questions are generally put in the "Extra Exercises" section at the end of each chapter. On occasions proofs are also not initially given, or relegated to the appendix as is the case with the standard-part function, and d(e^x)/dx. The foundations of the hyperreal numbers given in the book is weak, and exposition is relegated to another book: "Foundations of Infinitesimal Calculus" which is effectively only the proofs and theorems necessary for (and those which are part of) the book without other content.
What is it? It's a good book on the standard Calculus sequence. It has great breadth covering more than is typically in that sequence, and I think promotes good intuition. The infinitesimals seem to make the proofs given easier to understand, and makes the geometry more solid. To me there are times where things are not sufficiently explained even in terms of just establishing intuition, but I mostly fault myself for not understanding, and eventually come to an understanding.