Mereology:
Logic of parts and wholes.
Mereology was first seriously studied and developed by Lesniewski and
independently by Whitehead, although there are 19th Century predecessors
(Grassmann).
It differs from set theory, though it was intended, at least by Lesniewski,
to provide a basis for all of mathematics, just as set theory does.
A good introduction is Peter Simons: Parts.
