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 x and y, swapping x and y will not change the polynomial's value. These polynomials can be expressed in terms of the elementary symmetric polynomials, which are the building blocks of symmetric functions. There are several important types of symmetric polynomials, including homogeneous and complete symmetric polynomials. Homogeneous symmetric polynomials have all terms of the same degree, while complete symmetric polynomials are formed by summing all products of the variables taken a specific number of times. These concepts are fundamental in areas like algebra and combinatorics.