Yesterday I noticed on Twitter that Springer have made available quite a few classic books from their “Undergraduate Texts in Mathematics” and “Graduate Texts in Mathematics” freely available as PDFs. Some of these I paid good money for as an undergraduate and still have on my shelves and dip into occasionally.
A GitHub user “bishboria” has usefully made a hyperlinked list of all the books from these series that are available for free as a GitHub Gist here. If you are so inclined further down the page are shell scripts that you can run to automatically download all of them.
There is a great variety of books available, but if you only want to download one, in my opinion a book that is definitely worth having is Donald Estep’s “Practical Analysis in One Variable”. This is an amazing book that covers topics ranging from the natural numbers and the invention of negative numbers up to topics in analysis such as Weierstrass’ approximation theorem. Donald Estep is also interesting to follow on Twitter at @donestep1. As an aside he is also one of the authors of the books for the “Applied Mathematics: Body and Soul” project.