This lecture provides a comprehensive overview of volatility modeling in finance, covering fundamental concepts such as realized volatility, historical and implied volatility, and various estimation techniques including exponential moving averages and advanced estimators like the Garman-Klass and Yang-Zhang models. It also delves into stochastic process models like geometric Brownian motion, jump diffusion, and time-varying volatility models such as ARCH and GARCH, alongside practical time series forecasting methods and empirical case studies, highlighting their applications and comparative efficiencies.