The article provides a comprehensive review of supersymmetric quantum mechanics (SUSY QM), covering its theoretical formulation, applications, and extensions. It begins by discussing the Hamiltonian formulation of SUSY QM, including the factorization method and the connection between SUSY and the factorization method. The concept of shape invariance is introduced, which allows for the algebraic solution of certain potentials. The article then explores various applications of SUSY QM, such as the construction of isospectral potentials, the WKB approximation, and the solution of the Dirac equation. It also discusses the extension of SUSY QM to higher dimensions and the problem of singular superpotentials. The article concludes with a discussion on parasupersymmetric quantum mechanics, which generalizes SUSY QM to include parafermions. The review highlights the deep connections between SUSY QM and other areas of physics, such as stochastic processes and classical mechanics, and provides a detailed analysis of the mathematical structures underlying SUSY QM.The article provides a comprehensive review of supersymmetric quantum mechanics (SUSY QM), covering its theoretical formulation, applications, and extensions. It begins by discussing the Hamiltonian formulation of SUSY QM, including the factorization method and the connection between SUSY and the factorization method. The concept of shape invariance is introduced, which allows for the algebraic solution of certain potentials. The article then explores various applications of SUSY QM, such as the construction of isospectral potentials, the WKB approximation, and the solution of the Dirac equation. It also discusses the extension of SUSY QM to higher dimensions and the problem of singular superpotentials. The article concludes with a discussion on parasupersymmetric quantum mechanics, which generalizes SUSY QM to include parafermions. The review highlights the deep connections between SUSY QM and other areas of physics, such as stochastic processes and classical mechanics, and provides a detailed analysis of the mathematical structures underlying SUSY QM.