Here are some books I recommend:

General Mathematics/Math Team:

The Number Devil

The Joy of Mathematics, by Theoni Pappus

Flatland

Math Competitions:

Introduction to Geometry, by Richard Rusczyk,

Mandelbrot Morsels, Sam Vandervelde

AoPS Volume 2, Richard Rusczyk, Sandor Lehoczky

Undergraduate:

Algebra, Artin

A Walk Through Combinatorics, Miklos Bona