Beginning with a concise introduction on the constituents of matter (elementary particles, atomic nuclei, atoms and molecules), this course on the structure of matter focuses on the interaction of particles and radiation with matter. The course is divided into fourteen lectures with each ranging from physical fundamentals to current topics in subatomic and atomic research, thus making links to modern applications. Currently important topics such as channeling, the interaction between molecular ions and matter, and muon-catalyzed fusion are also discussed. The text is suitable as an introduction for graduate students and as a reference for scientists.