Chip-scale photonic circuits are dozens to thousands of optical elements integrated in a single chip to enable complex functionalities while reducing size, weight, and cost. The complexity of photonic circuits requires robust approaches for their analysis and optimization. Transmission matrix formalism makes the task of design both easy and fun. It allows a complex circuit to be broken into smaller blocks, and each block can be optimized separately to meet the requirements set by the circuit. This book introduces the formalism and shows how it is used for the analysis of devices and circuits. Layout and manufacturability of photonic integrated circuits and ways of improving them are also discussed.