At the same time the basic concepts of set theory are used throughout mathematics, while the subject is pursued in its own right as a speciality by a comparatively small group of mathematicians and logicians. It should be mentioned that there are also mathematicians using and promoting different approaches to the foundations of mathematics. The basic concepts of set theory are set and membership. A set is thought of as any collection of objects, called the members of the set. In mathematics, the members of sets are any mathematical objects, and in particular can themselves be sets.
Sets are one of the base concepts of mathematics.
A set is, more or less, just a collection of objects, called its elements. The notation is not self-explanatory. If you don't mind jumping ahead a bit, the subsets of a given set form a BooleanAlgebra under these operations. However, they aren't the only possible axioms, and in some senses are too restrictive. The above is more than a little confusing.