Imagine watching a stock price flicker every second of the trading day. If you tried to model that randomness with ordinary calculus—which works for smooth, predictable curves—you’d quickly get stuck. Real prices are jagged, not smooth. They need a different kind of math. This chapter introduces that math. We’ll move from thinking in discrete steps to continuous time, and learn how to describe, integrate, and differentiate random processes that never stop moving. By the end, you’ll see why geometric Brownian motion is the go‑to model for stock prices, and how Itô’s formula replaces the usual chain rule.