A set is a well-defined collection of distinct objects called elements. Sets can be represented in roster form ({1, 2, 3}), set-builder form ({x : x is a natural number, x < 4}), or Venn diagram form. The empty set (containing no elements) is a subset of every set. Key types: finite sets have a countable number of elements, infinite sets are countable (like natural numbers) or uncountable (like real numbers). Two sets are equal if they contain exactly the same elements — order and repetition do not matter in set notation. The universal set U contains all elements under consideration. The power set P(A) is the set of all subsets of A, with |P(A)| = 2^|A|. Set operations and their properties form the algebraic structure that underpins probability, logic, and discrete mathematics.