A set is a collection of distinct objects, which can be defined either through a roster method listing its elements or a set builder method using a rule to specify its elements. There are different ways to represent sets including through brackets, Venn diagrams, and notation of their size whether finite or infinite. Basic set operations include union, intersection, complement, and disjoint sets where union combines sets, intersection identifies shared elements, complement identifies elements not in the original set, and disjoint sets have no shared elements.