This paper provides a comprehensive review of Random Matrix Theory (RMT), focusing on both Hermitian and non-Hermitian random matrix ensembles. RMT is a statistical theory that describes the eigenvalue correlations of large matrices, which are important in various physical applications. The authors introduce ten different classes of random matrix ensembles, including the Wigner-Dyson ensembles, chiral ensembles, and Altland-Zirnbauer ensembles, each characterized by different symmetries and properties. They discuss the mathematical methods used to analyze these ensembles, such as orthogonal polynomials, Selberg's integral, the supersymmetric method, the replica trick, and resolvent expansion methods. The paper also explores the analogy between RMT and statistical mechanics, particularly the Dyson gas, which helps in understanding universality in eigenvalue correlations. Additionally, it covers applications of RMT in nuclear physics, quantum chaos, and other areas, highlighting the parameter-free agreement between theoretical predictions and experimental data. The review emphasizes the importance of RMT in understanding complex systems and the universal nature of spectral correlations.This paper provides a comprehensive review of Random Matrix Theory (RMT), focusing on both Hermitian and non-Hermitian random matrix ensembles. RMT is a statistical theory that describes the eigenvalue correlations of large matrices, which are important in various physical applications. The authors introduce ten different classes of random matrix ensembles, including the Wigner-Dyson ensembles, chiral ensembles, and Altland-Zirnbauer ensembles, each characterized by different symmetries and properties. They discuss the mathematical methods used to analyze these ensembles, such as orthogonal polynomials, Selberg's integral, the supersymmetric method, the replica trick, and resolvent expansion methods. The paper also explores the analogy between RMT and statistical mechanics, particularly the Dyson gas, which helps in understanding universality in eigenvalue correlations. Additionally, it covers applications of RMT in nuclear physics, quantum chaos, and other areas, highlighting the parameter-free agreement between theoretical predictions and experimental data. The review emphasizes the importance of RMT in understanding complex systems and the universal nature of spectral correlations.