Elementary books by good mathematicians I'm interested in elementary books written by good mathematicians.
For example:


*

*Gelfand (Algebra, Trigonometry, Sequences)

*Lang (A first course in calculus, Geometry)


I'm sure there are many other ones. Can you help me to complete this short list?
As for the level, I'm thinking of pupils (can be advanced ones) whose age is less than 18.
But books a bit more advanced could interest me. For example Roger Godement books: Analysis I & II are full of nice little results that could be of interest at an elementary level.

Not sure how easy an 18 year old might grasp this, but
Paul R. Halmos' Naive Set Theory is definitely a keeper. (obviously on set theory; relatively non-axiomatic)
This is a little more elementary and I think is definitely a good read especially since most high school students live in the world of pre-rigorous mathematics; I think everyone's first exposure to rigorous math is through proofs:
David C. Velleman's How to Prove it (introductory set theory and proof-writing)
EDIT: Age is not an indicator of ability.
