Irreligion is purported to be a summary of "why the arguments for god just don't add up" according to its cover. This is a fairly accurate summary of what the book contains.I bought this book because I had read a few of John Allen Paulos' columns and was entertained by him. The topic of Irreligion seemed interesting to me, and the book wasn't very expensive, long or intimidating.
I need to stop buying and reading books about atheism. Once you have read one, you have read them all. (I recommend "The God Delusion" as the best of the bunch) Richard Dawkins approaches atheism and religion through biology, Sam Harris through brain science, and Hitchens through philosophy and literature, for example. Paulos does it through statistics. I thought this would be a unique approach, but it somehow was not.
Irreligion is rebuttals to several (not new) arguments for the existence of god. The majority of the book is stuff I have read elsewhere. It is a nice (short, easy) summary of this stuff for people who haven't read all about it previously, but fails to say much new stuff. Most of it isn't even based on statistics, as touted. More logicy, proofy stuff. Meh.
Paulos does have one other thing going for him, as an atheist writer. He has tact. His arguments are very friendly and approachable, not condescending or sarcastic. I have heard some people are put off my the causticity of Dawkins and Harris. If so, Paulos might be your guy!
I would recommend this book to either someone who just can't get enough pro-atheist books, or to someone who was slightly curious about it but didn't want to commit to a longer, more intense (or insulting) book. I am sure Irreligion has its place in the atheism book ecosystem, but I personally didn't get a ton from it. To most people I would recommend The God Delusion by Richard Dawkins over Irreligion.