The essay offers a concise appraisal of a major mathematician's oeuvre, highlighting his habit of framing problems in their full generality and inventing tailored analytical tools. It summarizes work on discontinuous transformation groups and the uniformization of multivalued complex functions, developments in complex analysis and linear differential equations, and contributions to topology and celestial mechanics. The author also outlines methodological traits, critical remarks on physical theories, and philosophical reflections, and emphasizes the subject's inventive power, geometric intuition, and distinctive literary style.