This book is concerned with the methods by which the dynamics of endogenous economic growth systems may be analysed and numerically computed, and with the validation of such numerical computations through qualitative economic reasoning. The methods comprise linearization, phase-space analysis and a variety of numerical integration techniques. In particular, the book provides a detailed examination of the transitional dynamics (the movement from some current state towards a steady-state equilibrium) of the influential endogenous growth model from Paul Romer's 1990 Journal of Political Economy article: "Endogenous Technological Change".