Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures investigates third order rational difference equations by detailing the behavior of 225 special cases including boundedness, periodic nature, the global asymptotic stability of solutions, as well as extensions and generalizations. The methods developed to understand the dynamics of rational difference equations are useful to analyze equations in any mathematical model involving difference equations. Addressing period-two and period-three trichotomies, the book also presents various open problems and conjectures in order to stimulate future directions for research in the field.