Quadratic Reciprocity is a fundamental theorem in number theory that describes the relationship between the solvability of certain quadratic equations and prime numbers. Specifically, it provides criteria for determining whether a quadratic equation of the form x^2 \equiv p \mod q has solutions, where p and q are distinct odd prime numbers. The theorem was first conjectured by Leonhard Euler and later proved by Carl Friedrich Gauss in his work "Disquisitiones Arithmeticae." It consists of two main parts, known as the "reciprocity law," which states that the solvability of these equations depends on the congruences of the primes involved.