Cauchy's Integral Theorem states that if a function is holomorphic (complex differentiable) within and on a simple closed curve in the complex plane, then the integral of that function over the curve is zero. This means that the value of the integral does not depend on the specific path taken, as long as the path is closed and does not cross any singularities of the function. This theorem is a fundamental result in complex analysis and is named after the mathematician Augustin-Louis Cauchy. It lays the groundwork for many other important results, including Cauchy's Integral Formula, which provides a way to evaluate integrals of holomorphic functions.