Beyond Infinity by Eugenia Cheng (2017, ISBN 978-0-465-09481-3)
Subtitle-- An Expedition To The Outer Limits Of Mathematics.

A book for the general reader about infinity and set theory. Well written. Slow at first, but I found the later chapters more interesting. Contains many drawings explaining various aspects of the subject.

Purchased at Barnes on 2017-6-22 for 27.00$

To Infinity and Beyond by Eli Maor. ISBN 0-691-02511-8. Subtitled: A cultural history of the infinite. This book has four main sections. Infinity is discussed in terms of numbers, geometry, art and science. I think I enjoyed the numbers section the most. The art section discussed the art of M.C. Escher and tiling. Purchased at Powell's, 10.95.

One Two Three ... Infinity by George Gamow. Originally published in 1947, this copy was printed in 1967 and includes some revisions from about that time. I bought this book new in about 1968. I was in grade school at the time. I remember reading it and being fascinated by the big numbers (especially the descriptions of infinity) and the various descriptions of Relativity and Cosmogony. This particular edition of the book is probably a bit out of date, there is a more current Dover re-print, ISBN 0486256642. Still, I enjoyed re-reading it and would recommend it to anyone interested in learning about science. I was reminded about this book while reading The Pythagorean Theorem by Eli Maor. His book was so good that I bought a copy of his To Infinity and Beyond and in that book was a reference to this book. So I looked around in my boxes of books and found this book and decided to re-read it. Glad I did.

Infinity and the Mind, by Rudy Rucker. ISBN 0-691-00172-3. This is an excellent introduction to some complex ideas. Probably the reader who has little or no exposure to these ideas will find this book very difficult. Chapter titles are Infinity, All the Numbers, The Unnameable, Robots and Souls, The One and the Many, The Transfinite Cardinals, Godel's Incompleteness Theorems. I enjoyed this book (I have read it three times), but I find the Unnameable and the sections on Large Cardinals and Incompleteness difficult to understand.

The Mystery of the Aleph by Amir D. Aczel. ISBN 1-56858-105-X. The subtitle is Mathematics, the Kabbalah, and the Search for Infinity. This book is about the history of infinity. It is less technical than the David Foster Wallace book. Like that other book this one is mostly about Georg Cantor, but also covers Zeno (and other Greeks), Galileo, Gödel, Cohen and others. The book is well written and easy to read. The explanations of the more technical parts of the story are a bit over simplified, but still enjoyable for someone interested in this subject. This book plays up the idea that the study of infinity causes insanity.

Everything and More: A Compact History of ∞, By David Foster Wallace. ISBN 978-0-393-32629-1. This a really good book. A bit eccentric in style, but it works because the subject, infinity, is so complex. The story is mainly of Cantor's work in the modern theory of infinity, but it covers stuff from all periods of history, e.g., Zeno and other ancient Greeks to European mathematics of the 1600's and the discovery of Calculus (Leibniz and Newton.)
This book touches on many complex mathematical ideas, but doesn't get too bogged down with proofs, etc.