The list author says: "Here are some good books to checkout if you like Math at the Undergrad/Grad level (mostly undergrad).

I tried to pick books which were for the most part user-friendly (except for Rudin). I also only know of 1 differential equations book so I put it down (actually, there's one more I know of that Mathematicians think is good- which means it's not a good intro)."

"Best book ever for mathematical logic. The exposition is wonderful. His basic recursion theory is the best out there. He's a VERY rare combination, someone who teachs it well and knows what he is doing."

"This is a great "determinant free" book for the most part. It's on the theory side so maybe not for someone who hasn't had an intro. "computational" linear algebra course."

"I thought this book was out of print, but if this is what I am thinking of, it should be a great introduction to "Rings, Modules, and Linear Algebra." Very easy to follow (especially on things such as Jordan canonical form)."

"This book is great once you've had an intro. course. It's good for people starting upper div. probability (and for people thinking about being actuaries and taking the P1 exam). Ross has tons of examples of varying difficulty."

"If you've had a solid course in linear algebra (or similar course in understanding proofs), this book is a great introduction to algebra. It's a classic."

"I like this book. People seem to like the more modern book by Marker (which is superb). I'm a bit old-fashioned and still like Chang and Kiesler as well."

"I included this book because it's a classic. But, I don't know how well you will learn from it. The proofs are very slick. If you're looking for a read where you don't put effort in, then this is not the book for you."

"This book is great, but not necessarily a starting book (depends on what you like I guess). Most people will prefer Stewart, Rogawski, Sallas, etc for standard multivariable calc. After that and a little bit of linear algebra, this book would be fun."

"This book has good exercises (and answers). It's exposition is clear and concise. Greene is a great guy. He always wants you to see the idea (not just the details). Gamelin is excelent with mathematical prose for the non-mathematican (the mathematician as well)."

"Modern and clear. There's also a solutions manual in progress (not by the author) somewhere on the web for public display. I prefer this to Ahlfors (but then again some people would think I'm a moron for doing so)."

"As far as grad books go, this book is king if you want to learn the material quickly. I like this book much better than Hatcher, but, then again, I never seriously used Hatcher (so maybe I'm wrong)."

"I've always liked the Springer undergrad series. I guess at this level, it's more about how you say it. Most grad books seem to take the approach of "it's what you say" not "how you convey it." If only Springer had an undergrad version of its grad series."