Monte Carlo methods are a broad class of computational techniques based on repeated random sampling—known as replications—to compute numerical results. This chapter introduces both Monte Carlo and quasi-Monte Carlo methods, comparing their convergence rates and practical uses. Through fundamental examples such as the random walk, travelling salesman problem, and Monte Carlo integration, readers are guided from the basic principles to hands-on computational techniques. Key mathematical ideas—such as the law of large numbers and central limit theorem—are briefly discussed to illustrate the behavior of random walks and simulation results. This chapter sets the groundwork for the advanced topics explored in later chapters.