Abel's Theorem is a fundamental result in mathematics that deals with the convergence of infinite series. It states that if a series of functions converges uniformly on a closed interval, then the limit function is continuous. This theorem is particularly important in the study of power series and helps in understanding how functions behave when expressed as infinite sums. The theorem is named after the Norwegian mathematician Niels Henrik Abel, who made significant contributions to the field of analysis. Abel's Theorem provides a crucial link between the properties of series and the continuity of their limits, making it a key concept in mathematical analysis.