The paper presents a fundamental theory of noise which the authors believe to be physically perspicuous and from which all the well-established formulae used in practice can be deduced by direct mathematical argument. Since these formulae almost all relate to mean-square noise in linear circuits, the theory will not be applied here to other problems, although its ideas are valuable in attacking more complicated problems.The subject is discussed under the following headings: (1) Introduction; (2) the basic postulate and the fundamental equations; (3) the “mean theorem” and the “mean-square theroem” (4) the calculation of mean-square noise; (5) thermal noise; (6) application to valve and circuit noise; (7) space-charge effects; and (8) transit-time effects.