Literally, 'theory of parts'. Term introduced by the Polish logician Stanislaw Lesniewski (1886-1939) to cover a theory which used the whole/part relation as a substitute for the class-membership relation to deal with the structure of classes in ways that would avoid various difficulties connected with the vicious circle principle and the simple theory of types. (The term also has a technical use within the theory itself.)
The point about the whole/part relation is that, unlike class-membership, it is transitive; that is if a is a part of b, and b is a part of c, then a is a part of c.
The notion has also been used (by N Goodman, The Structure of Appearance (1951)) to deal with problems concerning stuffs (like water) or general qualities (like red): 'water' is taken to be a name for the total quantity of water in the universe (so that the Pacific Ocean counts as a part of water); similarly 'red', in naming the colour red, names the totality of red things, treated as a single large object split up over space.
P Simons, Parts (1987), ch. 1