Reference request: self-contained rigorous introductions to "cool" topics

Question

I am looking for some self-contained (i.e., providing all necessary background information) rigorous introductions to topics perceived as "cool" to propose to (really) advanced high school students specializing in math. For example, I am thinking about Invitation to Dynamical Systems by Scheinerman. Do you have any other ideas?

Answer 1

An Introduction to Mathematical Cryptography (Hoffstein, Pipher, Silverman) could fit the bill.

Answer 2

The Knot Book, by Colin C Adams is a good one.

Answer 3

Sets for Mathematics by Lawvere and Rosebrugh is a serious introduction to category theory, intended for high school students.

Answer 4

An Introduction to Abstract Algebra (Pinter) is rigorous but should be accessible to bright high school students who can handle proofs.