I first read this book half-way through A-Level and understood, at most 25% of the concepts contained within, it was well worth the read though. Having read the book again after completeing my first year at university, I can now say I understand at least 80% of the maths in this book.
The book is not a techincal mathematics book, there are no theorems and associated proofs etc, instead it is a look at the history of some of the most familiar parts of mathematics. Its a very interesting read, as you get more of feel for the history of the bits of mathematics that you use everyday.
The book also paints us a picture of the mathematicians that steer the subject, they are no longer just a name in a theorem, did you know that Galois died in pistol duel over a lady?
From here to infinity covers both classical and modern areas of mathematics, it stresses that mathematical theorems can never be outdated and replaced like scientific theorems (they can be wrong however). Ian Stewart briefly dips into chaos, computability and fractals, just enough to see if you're interested.
I would advise that to get the most from this book you should have at least done some university level mathematics, after all to understand the concept of non-standard analysis, you need to understand standard analysis.
If your a first year, get this book, and read it now, then read again in a year, and impress yourself with how much you've leaned.