[A recent answer](https://mathoverflow.net/questions/14311/maxspec-spec-radspec-or-why-not-look-at-all-radical-ideals/14319#14319) 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.)?



Good lattice theory books?
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.


