This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. Each chapter contains a section of open problems and conjectures, many of them ideal for research projects or Ph.D. theses. The techniques and results in this monograph are extremely useful in analyzing the equations in the mathematical models of various biological systems and other applications. Clear, simple, and direct exposition combined with thoughtful uniformity in the presentation make the book invaluable as a text as a reference for researchers, and as a supplement to every textbook on difference equations.