You have already met Brownian motion as the unpredictable, continuous random motion that models everything from stock prices to tiny particles in water. So far we have looked at its path properties, but we haven’t yet been able to “add up” a random amount of its wiggles over time. This chapter gives you the tool that makes that possible – the Ito stochastic integral. It is the foundation of stochastic calculus, and by the end you will understand how to build new random processes from Brownian motion while keeping the “no peeking into the future” rule intact.