It's a commonplace to state that while other sciences (like biology) may always need the newest books, we mathematicians also use to use older books. While this is a qualitative remark, I would like to get a quantitative result. So what are some "old" books that are still used?
Coming from (algebraic) topology, the first things which come to my mind are the works by Milnor. Frequently used (also as a topic for seminars) are his Characteristic Classes (1974, but based on lectures from 1957), his Morse Theory (1963) and other books and articles by him from the mid sixties.
An older book, which is sometimes used, is Steenrod's The Topology of Fibre Bundles from 1951, but this feels a bit dated already. Books older than that in topology are usually only read for historical reasons.
As I have only very limited experience in other fields (except, perhaps, in algebraic geometry), my question is:
What are the oldest books regularly used in your field (and which don't feel "outdated")?
Best Answer
Meet the Rudins: Baby Rudin (first published in 1953), Papa Rudin (whose oldest copyright I've been able to find dates back to 1966) and Grandaddy Rudin (1973 is the oldest reference I've found).