One of Jacobi's greatest accomplishments was his theory of elliptic functions and their relation to the elliptic theta function. This was developed in his great treatise "Fundamenta nova theoriae functionum ellipticarum" (1829), and in later papers in Crelle's Journal. Theta functions are of great importance in mathematical physics because of their role in the inverse problem for periodic and quasi-periodic flows. The equations of motion are integrable in terms of Jacobi's elliptic functions in the well-known cases of the pendulum, the Euler top, the symmetric Lagrange top in a gravitational field and the Kepler problem (planetary motion in a central gravitational field).