Books on Pre-Cantorian Infinity
Title Author Pub Date Publisher Amazon Rank Description
A Brief History of Infinity Paolo Zellini 2005 Penguin Global 698,926 Emphasis more on philosophy of infinity in mathematics than on the mathematics itself
Everything and More: A Compact History of Infinity David Foster Wallace 2003 W. W. Norton & Company 472,885 A survey of the mathematical treatment of the infinite from the beginnings of history up to the time of Cantor.
Fragments of Infinity: A Kaleidoscope of Math and Art Ivars Peterson 2001 Wiley 145,696 This is a unique book that looks at artistic creations inspired by mathematical formulas of various kinds.
From Five Fingers to Infinity: A Journey Through the History of Mathematics Frank Swetz 1994 Open Court Publishing Company 763,660 Emphasis on the history of mathematical thought, with the concept of the infinite as a common thread.
From Zero to Infinity: What Makes Numbers Interesting Constance Reid 2006 A K Peters, Ltd 171,627 Takes the angle of focussing on a few particular numbers as a device for introducing mathematical ideas to the layman. 
Gödel, Escher, Bach: The Eternal Golden Braid Douglas Hofstadter 1979 republished: 1999 Basic Books 700 Hofstadter won the Pulitzer Prize in 1979 for this work, which introduces common themes woven thorugh the fields of mathematical logic, the work of Escher, and the compositions of Bach.
Infinity: The Quest to Think the Unthinkable Brian Clegg 2003 Carroll & Graf Publishers 616,115 Beginner’s book about how the infinite plays a role in the development of modern science
Keys to Infinity Clifford A. Pickover 1997 Wiley 1,147,354 A book of brain-teaser puzzles that are tangentially related to the concept of infinity
Numbers and Infinity: A Historical Account of Mathematical Concepts Ernst Sondheimer 2006 Dover Publications 643,696 An introduction to mathematical ideas.
One Two Three . . . Infinity: Facts and Speculations George Gamow 1988 Dover Publications 27,303 A friendly introduction to math and science, intended for the younger mind (pre-high school).
Playing With Infinity Rozsa Peter 1976 Dover 705,407 User-friendly intro to mathematical ideas including some of the history behind the modern understanding of mathematical infinite.
The Art of the Infinite: The Pleasures of Mathematics Robert and Ellen Kaplan 2003 Oxford University Press 558,603 Introduction to mathematical ideas leading up to “infinity”. They declare "Mathematics is the art of the infnite."
To Infinity and Beyond Eli Maor 1991 Princeton University Press 96,358 Examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences
Understanding Infinity: The Mathematics of Infinite Processes A. Gardiner 2003 Dover Publications 915,219 A step-by-step intro for the beginner to calculus ideas. "Infinite" here has to do with the "limit" concept in calculus
Uses of Infinity Leo Zippin 1962 Dover Publications 802,959 Introduces calculus concepts for the beginner. Leo Zippin is a well-known mathematician.