Scientific computing and statistical applications rely heavily on computer-generated random numbers, forming the basis for methodologies such as random sampling and Markov Chain Monte Carlo (MCMC). This chapter explores foundational methods of pseudo-random number generation, emphasizing Inverse Transform Sampling as a core technique. Uniform random number generators (RNGs) serve as the building blocks for these methods, aiming to produce sequences that closely approximate true randomness. Key properties such as efficiency and long-period length are examined, leading to an in-depth discussion of Linear Congruential Generators (LCGs). The chapter further presents theoretical insights into the behavior and effectiveness of LCGs in computational settings.