Where can I learn about the lattice of partitions?

Question

A set $P \subseteq \mathcal{P}(X)$ is a partition of $X$ if and only if all of the following conditions hold:

1. $\emptyset \notin P$
2. For all $x,y \in P$, if $x \neq y$ then $x \cap y = \emptyset$.
3. $\bigcup P = X$

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.

Answer 1

G. Birkhoff, Lattice Theory. Providence, Rhode Island, 1967,

Chapt.4, sec.9.

Answer 2

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.

Answer 3

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.