I recommend a single book which doesn't require any knowledge about mathematics:

Ebbinghaus et. al.: "Numbers"

Full list of authors: Heinz-Dieter Ebbinghaus (Author), Hans Hermes (Author), Friedrich Hirzebruch (Author), Max Koecher (Author), Klaus Mainzer (Author), Jürgen Neukirch (Author), Alexander Prestel (Author), Reinhold Remmert (Author), John H. Ewing (Editor), H.L.S. Orde (Translator), K. Lamotke (Introduction))

It is a translation from the german book "Zahlen", which I read with pleasure during my first year at the university. All authors are german mathematicians known for their wonderful writing.

The book teaches you a lot about different number systems, like the complex numbers, the Cayley numbers, nonstandard numbers and so on. It also connects these topics to other topics in mathematics, so it provides a beautiful example-based introduction to mathematics. It doesn't stop at basic material, so you can revisit this book after one or two years of university courses, and with a new perspective, learn something new again!

I have to warn you that it's not a book about number theory, although it touches elementary number theory preliminaries at various places and I guess you should read something like it before reading any serious number theory.

The book is full of historical remarks and motivational paragraphs. Nevertheless, it's written in a clear and formally correct way (not the sometimes difficult "colloquial style" found in American math introduction books).

If you're interested in infinite series, this book might be especially good for you.

See Amazon and Google Books to skim the table of contents.