Symmetric polynomials are a special class of polynomials that remain unchanged when the variables are permuted. For example, if you have a polynomial in variables x₁, x₂, ..., xₙ, it is symmetric if swapping any two variables does not alter the polynomial's value. Common examples include the sum of the variables and the product of the variables. These polynomials play a crucial role in various areas of mathematics, including algebra, combinatorics, and representation theory. They are particularly important in the study of roots of polynomials and can be expressed in terms of elementary symmetric polynomials, which are the building blocks of all symmetric polynomials.