Mathematics before Leonhard Euler -- Brief biographical sketch and career of Leonhard Euler -- Euler's contributions to number theory and algebra -- Euler's contributions to geometry and spherical trigonometry -- Euler's formula for polyhedra, topology and graph theory -- Euler's contributions to calculus and analysis -- Euler's contributions to the infinite series and the zeta function -- Euler's beta and gamma functions and infinite products -- Euler and differential equations -- The Euler equations of motion in fluid mechanics -- Euler's contributions to mechanics and elasticity -- Euler's work on the probability theory -- Euler's contributions to ballistics -- Euler and his work on astronomy and physics.