This book introduces a method for modeling engineered systems to persons with a background in mathematics but little or no experience in engineering or physics. The idea emerged from a graduate course that the author taught in the mathematics department at the University of Memphis. Using the method presented here, his mathematics students finished the semester being able to look at an engineering diagram and write its governing equations. The importance of teaching mathematics students the essentials of systems modeling was highlighted in a Society for Industrial and Applied Mathematics (SIAM) Review letter by Ulrich Rude, Karen Willcox, Lois Curfman McInnes, and Hans De Sterck (Research and Education in Computational Science and Engineering, SIAM Review, vol. 60, no. 3, pgs. 707-754, 2018). They argue that undergraduate and graduate education in mathematics must include "simulation and modeling, including ... physics-based models". This book meets that requirement with a modeling method that can be grasped in its essentials as a set of rules for constructing graphs. Once the essentials are firmly in hand, you will learn how the physical interpretation of a graph allows these rules to be translated into specific engineering domains: electrical and hydraulic circuits, translating and rotating planar mechanical systems, and models that are a mixture of these domains.