As this my first post, I'm not sure if this is the right place to ask this question. But textbooks are learning materials, so I think it's alright. I enjoy learning new things in math, but textbooks are very expensive. I'd really hate to spend $100+ on a book, only find out that it isn't what I was looking for. So I do a lot of research online like reading customer reviews on amazon and related sites, wiki references, things like that. Then I thought 'Why not post a thread on Physics Forums?' Since this is a site for math and the sciences, there are bound to be people who have taken advanced math courses and have used enough books to know which ones work and which ones don't. So my question is this: Which book(s) are the best (i.e. in terms of ease of use, continuity of thought, logical progression, worked examples, number of typos, broad mix of problems) in their subjects (i.e. vector calculus, tensor calculus, ODE, PDE, real/complex analysis, number theory) I am particularly interested in real/complex analysis, ODE, and PDE as I am having the hardest time reseaching books for these subjects. As to complex analysis, most of my reseach seems to suggest "Complex Variables: Introduction and Applications" by Ablowitz is an excellent textbook. Same thing for "Visual Complex Analysis" by Needham. For ODEs, some people say "Elementary DE and Boundary Value Problems" by Boyce is a good book. Some people say nope, unless I get the 8th Ed. Still others say to avoid it all together. And PDE is even worse. There seems to be a million books out there, and just as many opinions; each one is different. Any advice or opinions will be greatly appreciated!!