Explore advanced mathematical concepts in this lecture from the Workshop on "Algebraicity and Transcendence for Singular Differential Equations" where Michael Singer delves into the third installment of Differential Galois Theory and the Algebraicity of Solutions. Gain deep insights into the intersection of differential equations and Galois theory, examining how these mathematical frameworks interact to determine the algebraic nature of solutions. Learn from this 90-minute presentation delivered at the prestigious Erwin Schrödinger International Institute for Mathematics and Physics (ESI), which forms part of a comprehensive workshop series exploring singular differential equations.