Where can I learn about the lattice of partitions? A set $P \subseteq \mathcal{P}(X)$ is a partition of $X$ if and only if all of the following conditions hold:


*

*$\emptyset \notin P$

*For all $x,y \in P$, if $x \neq y$ then $x \cap y = \emptyset$.

*$\bigcup P = X$


I have read many times that the partitions of a set form a lattice, but never really considered the idea in great detail. Where can I learn the major results about such lattices? An article recommendation would be nice.
I'm also interested in the generalization where condition 3 is disregarded.

George Grätzers book General Lattice Theory has a section IV.4 on partition lattices,
see page 250 of this result of Google books search. A more recent version of the book is called Lattice Theory: Foundation.
