This book studies 1-D and 2-D solutions of discrete and continuous analogue dynamical systems and identifies their intrinsic differences. It starts by introducing discrete dynamical systems before comparing them to continuous analogue ones. It studies in some depth periodic and chaotic-type solutions of quadratic and cubic equations and the harvesting/fishing effect on non-periodic and periodic solutions of populations models based on them. Considerations about the stability of the solutions are critical in their study. It contains examples of applications to accounting, pharmacology, harvesting/fishing strategies, economic and population models and historical battles.