Phononics: Interface Transmission Tutorial Book Series provides an investigation of modern systems that includes a discrete matrix description. Classical continuous systems relying on the use of differential equations are recalled, showing that they generally have a specific limit on their corresponding modern matrix formulation. A detailed description of the mathematical languages that enables readers to find the composite system linear transmission properties is provided in the appendix. The physical model is described with exacting detail, and the bibliography is built to cite—in chronological order—all the scientists that have contributed over many years. Each volume is written with the aim of providing an up-to-date and concise summary of the present knowledge of interface transmission science, thus fostering the exchange of ideas among scientists interested in different aspects of interface transmission. The book serves as an introduction to advanced graduate students, researchers, and scientists with little study on the subject, and is also useful to help keep specialists informed on general progress in the field.