Definition:Set of Sets

Definition
A set of sets is a set, whose elements are themselves all sets.

Those elements can themselves be assumed to be subsets of some particular fixed set which is frequently referred to as the universe.

Also known as
Many sources (perhaps still feeling the wrath of the cane from schoolteachers of English) feel uncomfortable about referring to a set of sets and use a synonym instead.

Thus you will find terms such as collection of sets, family of sets, assembly of sets - it goes on and on.

Take care when you see class of sets, because in modern set theory a class is a subtly different object from a set.
 * Beware the following:

Also note that some books on, for example, topology and analysis will use the word family of sets to mean set of sets, whereas the technically accurate definition for (indexed) family in recent times is a subtly different concept.

A system of sets, or a set system, is also defined as a set whose elements are themselves all sets, but the implication here is that the sets in question are augmented by the various operations, thus turning such sets of sets into algebraic structures.