Lattice theory and the theory of ordered sets are experiencing a renaissance because these fields clearly offer a tremendous array of exciting questions, with wide-ranging applications to such fields as theoretical computer science (the semantics of programming languages), image analysis (mathematical morphology), cryptology (secret sharing), epidemiology, economics (monotone comparative statics; the stable marriage problem), quantum physics (quantum gravity and the logic of quantum mechanics), linguistics, political science, sociology, chemistry, and so on. This course will not discuss applications, but instead will go through basic aspects of lattice theory, including, for instance, Birkhoff's theorem and Priestley duality for distributive lattices, and Dilworth's theorem for modular lattices; it will also touch on some open problem areas, such as the fixed point property.
B. A. Davey and H. A. Priestley, Introduction to Lattices and Order (second edition), Cambridge University Press, 2002. ISBN 0521784514
J. B. Nation, Notes on Lattice Theory, available free on-line at http://www.math.hawaii.edu/~jb/books.html.