Plato on Geometry and the Geometers -- Topology and Biology: From Aristotle to Thom -- Time and eriodicity from Ptolemy to Schrödinger: Paradigm Shifts vs Continuity in History of Mathematics -- Convexity in Greek Antiquity -- On the Concept of Curve: Geometry and Algebra, fromMathematicalModernity to MathematicalModernism -- From Euclid to Riemann and Beyond: How to Describe the Shape of the Universe -- A Path in History, from Curvature to Convexity -- The Axiomatic Destiny of the Theorems of Pappus and Desargues -- Projective Configuration Theorems: Old Wine into New Wineskins -- Poincaré’s GeometricWorldview and Philosophy -- Perturbing a Planar Rotation: Normal Hyperbolicity and Angular Twist -- René Thom and an Anticipated h-Principle -- Rigid and Flexible Facets of Symplectic Topology -- Flat Affine, Projective and Conformal Structures on Manifolds: A Historical Perspective -- Basic Aspects of Differential Geometry -- The Global Study of Riemannian-Finsler Geometry -- The Poincaré Conjecture and Related Statements -- A Glimpse into the Problems of the Fourth Dimension -- Memories fromMy Former Life: The Making of a Mathematician -- Index.