Ensuring the reliability of pseudo-random number generators requires rigorous evaluation, with the spectral test being a key analytical tool. This chapter introduces the spectral test as a method for assessing the uniformity of LCGs and MRGs, offering a quantitative means of ranking generator quality. Key theoretical aspects, such as lattice structure and equi-distribution, are explored in detail. Challenges associated with high-order MRGs, particularly in computational feasibility, are also discussed. The chapter concludes by setting the stage for an improved spectral test methodology, which will be developed further in subsequent discussions.