Introductory text for lattice theory

online-resources reference-request book-recommendation lattice-orders

What would be your recommendation for the text which could be useful for someone starting with lattice theory? Suggestion for both books and online materials/lecture notes are welcome.

This was asked as a part of this question and I did not like that it was combination of two different questions. (One of them on geometric modular lattices and the other one about text recommendation.)

I don't expect the user to post a follow-up question, since he was not seen at MSE for some time. I think that this could be a useful for some users here, so I've decided to post it myself.


I would recommend Gratzer's Lattice Theory: Foundations (latest edition 2010). It's exhaustive, lots of problems are included and there are also appendices on recent research. Also you can try checking more brief "A notes on lattice theory" by J.B.Nation (available for free on his website).


If you are looking for an introductory textbook I strongly recommend the following book:

  • B. A. Davey and H. A. Priestley, "Introduction to lattices and order", CUP, http://books.google.es/books?id=vVVTxeuiyvQC

Check the following:

Roman,Steven: "Lattices and Ordered Sets", Springer; Google books link

Blyth, T.S.: "Lattices and Ordered Algebraic Structures" , Springer; Google books link

Roggenkamp, Klaus - Huber-Dyson, Verena : "Lattices over Orders" , Springer


I found D. E. Rutherford's "Introduction to Lattice Theory" quite worth the effort.

It's available free from archive.org

It's rigorous and it takes short detours in areas of application. (which you may skim or skip depending on focus). I loved it. All 120 pages.

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