The Renaissance. Cardano. Solution of qubic equation. Complex numbers. Invention of logarithms. Fermat and Descartes. Analytic geometry. Number theory. Probability. The limit concept. Newton and Leibnitz. The Principia. Probability and infinite series. Development of calculus. Age of Euler. D’Alembert. Lagrange. Monge. Laplace. Gauss and Cauchy. Noneuclidean geometry. Lobachevskiy. Abel, Jacobi, Galois. Projective geometry. Riemannian geometry. Felix Klein. Analysis. Riemann. Mathematical physics. British Algebra. Algebraic geometry. Poincare and Hilbert. Topology. Aspect of Twentieth Century.