Unrivaled math classics that would be of practical benefit to the upcoming generation? I'm often impressed that top mathematicians in a given field seem to have not only a knowledge of the "state of the art" of their subfield, but also a knowledge of the history of the field and thus the seminal books/papers in the field.
In this direction, I would love to have a list of classic math texts (books, especially) that rate today not as mere historical curiosities, but that would be of benefit to a graduate student to read as a first introduction to a given field. Thus in some sense I'm asking for classic books that have not been rivaled or replaced. Are there such books? I'm told that Weyl's The Classical Groups is such a book. Are there others?
 A: Well, well, this is a dangerous question. 
I'll venture to post an answer, nonetheless. 
After reading your question for the first time, I thought I'd be able to name many books. But after thinking about it for a while, my personal (very subjective) list of books qualifying esp for 'classics' which (still) may serve as 'a first introduction to a given field' to a 'graduate student' for now reduces to


*

*Richard Courant's 'Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces'

*J. Milnor/ J.T. Stasheff: 'Characteristic Classes'

*J. Milnor: 'Morse theory'

*David Gilbarg, Neil S. Trudinger: 'Elliptic Partial Differential Equations of Second Order'

*Walter Rudin's 'Functional analysis'

*Ingrid Daubechies: 'Ten Lectures on Wavelets'


with the title leaving no doubt which field might be addressed in each of the books. I'm particularly unhappy to recognize that I'm not able to add a book dedicated to differential geometry to the list.
Some of these may not yet be considered classics.
