Itô calculus is a branch of mathematics that extends traditional calculus to include stochastic processes, which are systems that evolve randomly over time. It was developed by Japanese mathematician Kiyoshi Itô in the 1940s and is widely used in fields like finance, physics, and engineering to model uncertainty and randomness. The core concept of Itô calculus involves the integration of functions with respect to Brownian motion, a mathematical representation of random movement. This allows for the analysis of complex systems where uncertainty plays a significant role, enabling better predictions and decision-making in various applications.