A recent answer motivated me to post about this. I've always had a vague, unpleasant feeling that somehow lattice theory has been completely robbed of the important place it deserves in mathematics – lattices seem to show up everywhere, the author or teacher says "observe that these ____ form a complete lattice" or something similar, and then moves on, never to speak of what that might imply. But, not currently knowing anything about them, I can't be sure. What would be a good place to learn about lattice theory, especially its implications for "naturally occurring" lattices (subgroups, ideals, etc.)?
[Math] Good lattice theory books
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Best Answer
A good, user-friendly, modern, introductory textbook is Davey and Priestley's Introduction to Lattices and Order.
Incidentally, Gian-Carlo Rota used to say much the same thing as you, Zev: that lattice theory had been robbed of its rightful place in mathematics.