This paper introduces supersymmetry (SUSY) in quantum mechanics, demonstrating how it can be used to construct new exactly solvable potentials from existing ones. Given a solvable quantum mechanical problem with n bound states, one can construct new exactly solvable potentials with n-1, n-2, ..., 0 bound states. The relationship between the eigenvalues, eigenfunctions, and scattering matrix of SUSY partner potentials is derived, and a class of reflectionless potentials is explicitly constructed. The operator method used to solve the one-dimensional harmonic oscillator is extended to a class of potentials called shape-invariant potentials, which include almost all solvable problems in standard quantum mechanics textbooks. It is shown that given any potential with at least one bound state, one can construct a continuous family of potentials with the same eigenvalues and scattering matrix. The SUSY-inspired WKB approximation is discussed, showing that it is exact for shape-invariant potentials and for the ground state. New exactly solvable periodic potentials are constructed using SUSY quantum mechanics. The paper also discusses the relationship between SUSY partner potentials in the context of scattering and reflectionless potentials, and shows how the shape-invariance condition can be used to generalize the operator method for solving the harmonic oscillator to a broader class of solvable potentials. The paper concludes with a discussion of the classification of solutions to the shape-invariance condition and the discovery of new shape-invariant potentials.This paper introduces supersymmetry (SUSY) in quantum mechanics, demonstrating how it can be used to construct new exactly solvable potentials from existing ones. Given a solvable quantum mechanical problem with n bound states, one can construct new exactly solvable potentials with n-1, n-2, ..., 0 bound states. The relationship between the eigenvalues, eigenfunctions, and scattering matrix of SUSY partner potentials is derived, and a class of reflectionless potentials is explicitly constructed. The operator method used to solve the one-dimensional harmonic oscillator is extended to a class of potentials called shape-invariant potentials, which include almost all solvable problems in standard quantum mechanics textbooks. It is shown that given any potential with at least one bound state, one can construct a continuous family of potentials with the same eigenvalues and scattering matrix. The SUSY-inspired WKB approximation is discussed, showing that it is exact for shape-invariant potentials and for the ground state. New exactly solvable periodic potentials are constructed using SUSY quantum mechanics. The paper also discusses the relationship between SUSY partner potentials in the context of scattering and reflectionless potentials, and shows how the shape-invariance condition can be used to generalize the operator method for solving the harmonic oscillator to a broader class of solvable potentials. The paper concludes with a discussion of the classification of solutions to the shape-invariance condition and the discovery of new shape-invariant potentials.