Everything and More: A Compact History of Infinity

I particularly enjoyed _Everything and More: A Compact History of Infinity_ by David Foster Wallace. It gave me a new appreciation of not only the last two centuries of math, but also the english language and the abuse of sentence structure, asides, and footnotes[1][2][3] for educational and entertainment purposes. [1] so [2] many [3] footnotes[a] [a] Which, I must say, I found interesting and informative[b] [b] If a bit excessively nested.

+1 on DFW's book. It's odd, and really it's more a discussion on the history of modern mathematics than an in depth explanation of the concepts themselves, but it is a great read. I wrote a short review after reading it, which you might be interested in checking out: https://faingezicht.com/articles/2017/10/27/infinity/

I appreciated DFW's book for even attempting to do a popular treatment of what we would now call the history of real analysis. But there were some serious technical problems with it: http://www.ams.org/notices/200406/rev-harris.pdf

I clicked on this topic in order to make this suggestion. To expand on it a little bit, I was a math major and read Spivak's 'Calculus' after I had already taken real analysis. I found it delightful - it really approaches the topics from first principles and unlike many calculus textbooks actually goes through the effort of presenting proofs of the theorems. Highly recommended. As some recreational reading, less suiting the original request, I very much enjoyed David Foster Wallace's 'Everything and More: A Compact History of Infinity' (http://www.amazon.com/Everything-More-Compact-History-Infini... (http://www.amazon.com/Everything-More-Compact-History-Infinity/dp/0393339289/)). DFW is not for everyone, but I enjoyed it a lot. Maybe just check it out of the library first to see if it's for you.