The paradoxical nature of infinity has puzzled thinkers throughout the ages - an early example is Zeno's paradox. But Achilles in the Quantum Universe:The Definitive History of Infinity
, by Richard Morris, doesn't try to bamboozle the reader. Rather it gives a clear explanation of how such puzzles have occurred, and of the proposed solutions. Infinity is a mathematical concept, which some might think is unrelated to the real world. Naturally this book mentions mathematical ideas of infinity, such as infinitesimals and the work of Cantor, but its emphasis is on the occurence of infinities in physics, and how to get rid of them.
The book takes a look at quantum theory - at how it was introduced to get rid of the infinities of the ultraviolet catastrophe, and how later renormalisation tackled the infinities of quantum field theory. Morris goes on to deal with special relativity, where travelling at the speed of light leads to troublesome infinities, and at general relativity, where a black hole can compress matter to infinite density. There is plenty of discussion of cosmology, and what it means for the universe to be infinite. If you're looking for an easy to read account dealing with some of the troublesome parts of modern physics then you'll find this book to be very helpful.