Below are the noteworthy books suggested in comments to my last post: “Books with Longevity”. (I could not find good photos of Grothendieck’s EGA and SGA, published by publications IHES) Thanks for sharing them!
The intention of any worthy math book is to communicate a collective understanding of a subject by experts to potential future practitioners, but is it just me, or is there sometimes something more personal that happens between author and reader? Some books seem to “talk” to you. They can make you smile for the beauty that they reveal (examples for me are David Mumford’s Lectures on Curves on an Algebraic Surface, or Emil Artin’s Galois Theory), or they can egg you on with challenging problems leading you to deeper understanding (Attiyah and MacDonald’s Introduction to Commutative Algebra comes to mind).
On a more pragmatic level, as one comment pointed out, it is also important for books to be useful for teaching. That will be a topic for a future post.