The Multiplicative Weights Update Method is a meta-algorithm that unifies various algorithms in fields like machine learning, optimization, and game theory. It maintains a distribution over decisions and updates weights based on payoffs, aiming to achieve a total payoff comparable to the best decision in hindsight. The algorithm is simple, efficient, and applicable to a wide range of problems, including game theory, convex optimization, and online learning. It uses an exponential potential function for analysis and has a running time proportional to $1/\varepsilon^2$. The method is closely related to the "Hedge" algorithm and has been independently rediscovered in various contexts. It provides a constructive approach to LP duality and is useful in algorithms courses due to its simplicity and broad applicability. The paper surveys the algorithm, its variants, and applications, including the Winnow algorithm, zero-sum game solving, and packing/covering LPs. It also discusses the analysis using KL-divergence and provides bounds for different scenarios. The algorithm is shown to be effective in solving various optimization and game-theoretic problems with efficient running times.The Multiplicative Weights Update Method is a meta-algorithm that unifies various algorithms in fields like machine learning, optimization, and game theory. It maintains a distribution over decisions and updates weights based on payoffs, aiming to achieve a total payoff comparable to the best decision in hindsight. The algorithm is simple, efficient, and applicable to a wide range of problems, including game theory, convex optimization, and online learning. It uses an exponential potential function for analysis and has a running time proportional to $1/\varepsilon^2$. The method is closely related to the "Hedge" algorithm and has been independently rediscovered in various contexts. It provides a constructive approach to LP duality and is useful in algorithms courses due to its simplicity and broad applicability. The paper surveys the algorithm, its variants, and applications, including the Winnow algorithm, zero-sum game solving, and packing/covering LPs. It also discusses the analysis using KL-divergence and provides bounds for different scenarios. The algorithm is shown to be effective in solving various optimization and game-theoretic problems with efficient running times.