This book is concerning to a Differential Galois (Picard-Vessiot) Theory point of view of the Supersymmetric Quantum Mechanics. The main object is the non-relativistic stationary Schrodinger equation, where are introduced the concepts of Algebraic Spectrum and Hamiltonian Algebrization. Using the Kovacic's Algorithm and the Hamiltonian Algebrization are analyzed Darboux transformations, Crum iterations and supersymmetric quantum mechanics, including their Algebrized Versions from a Galoisian approach. In particular are obtained the ground state, eigenvalues, eigenfunctions, the differential...