Order Theory (subject)
Order theory is the study of certain kinds of relations on sets. Abstract algebra covers the case of a set equipped with functions (which are right-unique relations that map everything in their domain to something), order theory deals instead with relations that are at the very least, transitive and then branches off into lattices - which is studying the directed graphs (or digraphs) that result from various kinds of orderings, called lattice theory.
Some order theory is desired for parts of analysis, for this I recommend the reader know at least about partial orderings and posets, this is because topics like limits require some notion of ordering, however since year 2 children are taught to "pretend [ilmath]<[/ilmath] is a crocodile, it wants to eat the bigger number" and is fully aware that [ilmath]5<2[/ilmath] and such. However it cannot hurt.
The order theory project contains: