Based around a theme of the construction of a game engine, this textbook is for final year undergraduate and graduate students, emphasising formal methods in writing robust code quickly. This book takes an unusual, engineering-inspired approach to illuminate the creation and verification of large software systems. Where other textbooks discuss business practices through generic project management techniques or detailed rigid logic systems, this book examines the interaction between code in a physical machine and the logic applied in creating the software. These elements create an informal and rigorous study of logic, algebra, and geometry through software. Assuming prior experience with C, C++, or Java programming languages, chapters introduce UML, OCL, and Z from scratch. Extensive worked examples motivate readers to learn the languages through the technical side of software science.