1 Geometry: The Parallel Postulate -- 1.1 Introduction -- 1.2 Euclid's Parallel Postulate -- 1.3 Legendre's Attempts to Prove the Parallel Postulate -- 1.4 Lobachevskian Geometry -- 1.5 Poincaré's Euclidean Model for Non-Euclidean Geometry. -- 2 Set Theory: Taming the Infinite -- 2.1 Introduction -- 2.2 Bolzano's Paradoxes of the Infinite -- 2.3 Cantor's Infinite Numbers -- 2.4 Zermelo's Axiomatization -- 3 Analysis: Calculating Areas and Volumes -- 3.1 Introduction -- 3.2 Archimedes' Quadrature of the Parabola -- 3.3 Archimedes' Method -- 3.4 Cavalieri Calculates Areas of Higher Parabolas -- 3.5 Leibniz's Fundamental Theorem of Calculus -- 3.6 Cauchy's Rigorization of Calculus -- 3.7 Robinson Resurrects Infinitesimals -- 3.8 Appendix on Infinite Series -- 4 Number Theory: Fermat's Last Theorem -- 4.1 Introduction -- 4.2 Euclid's Classification of Pythagorean Triples -- 4.3 Euler's Solution for Exponent Four -- 4.4 Germain's General Approach -- 4.5 Kummer and the Dawn of Algebraic Number Theory -- 4.6 Appendix on Congruences -- 5 Algebra: The Search for an Elusive Formula -- 5.1 Introduction -- 5.2 Euclid's Application of Areas and Quadratic Equations -- 5.3 Cardano's Solution of the Cubic -- 5.4 Lagrange's Theory of Equations -- 5.5 Galois Ends the Story -- References -- Credits.