I cannot recommend Dover Publications highly enough! They have many good books and a few great ones…
One I recently bought is The Nature and Power of Mathematics by Donald M. Davis.
This book begins in relatively familiar territory, Greek mathematics, and includes an excellent discussion of π.
From there, the book discusses Non-Euclidean geometry, number theory, cryptography, and fractals, doing an excellent job of bridging old and new. The section on cryptography is an excellent introduction to this important topic.
