Introduction Never in the history of mathematics has a mathematical theory been the object of such vociferous vituperation as lattice theory. Dedekind, Jónsson, Kurosh, Malcev, Ore, von Neumann, Tarski, and most prominently Garrett Birkhoff have contributed a new vision of mathematics, a vision that has been cursed by a conjunction of misunderstandings, resentment, and raw prejudice. The hostil...

During the last 100 to 150 years, it has become common practice for mathematicians to consider collecting numbers (and/or other objects) into a single conglomerate. This point of view in fact permeates much of higher level mathematics. As such, students of mathematics should have a …rm grip on the underlying ideas of how these conglomerates behave. These conglomerates are typically called sets ...