A concise treatment of angular momentum by an important American physicist, this major work was first published under the auspices of the United States Atomic Energy Commission in 1952 and is finally available to a general audience of students and professionals in the field. Advanced undergraduates and graduate students of physics will particularly benefit from its teachings. One of the most prominent American physicists of the twentieth century, Julian Schwinger (1918-94) taught at Harvard, MIT, and UCLA, among other institutions. In addition to his many other awards, Schwinger, jointly with Richard Feynman and Shinichiro Tomonaga, received the Nobel Prize in Physics in 1965 for his work in quantum electrodynamics.