Newton's Identities are a set of equations that relate the power sums of the roots of a polynomial to its coefficients. Specifically, they connect the sums of the roots raised to various powers to the elementary symmetric sums of the roots. This relationship helps in understanding the properties of polynomials and their roots. These identities are particularly useful in algebra and number theory, as they provide a systematic way to calculate the sums of powers of roots without directly finding the roots themselves. They are named after Sir Isaac Newton, who made significant contributions to mathematics and physics in the 17th century.