This volume presents a mathematical analysis of cumulative processes of economic growth. In continuous time, the fundamentals of economic growth models are expressed by systems of nonlinear differential equations. With homogeneous dynamic systems as the unifying mathematical framework, the long-run stability properties and the phase portraits of the solutions to classical, neoclassical and Keynesian growth models are analyzed. The general structure and the solutions of two-sector growth models are also treated, with special attention given to output composition and factor allocation issues involved in general equilibrium dynamics. Among other results, this work shows that the dynamic structures and the kinematics of prototype growth models are globally robust. The monograph is divided in two sections: (1) Basic Economic Growth Models -- An Axiomatic Approach; (2) Basic Dynamic Systems. For scholars in economics and applied mathematics; recommended as a reference book for researchers and as a supplementary graduate textbook in economics and mathematics. A familiarity with calculus, ordinary differential equations, and the basic concepts of linear algebra is assumed.