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.

The Logic of Partitions: Introduction to the Dual of the Logic of Subsets
I just stumbled upon it a couple of days ago, but it looks to be a great reference.
