This text is intended for scientists engaged in the measurement of weak alpha, beta, and gamma active samples; in health physics, environmental control, nuclear geophysics, tracer work, radiocarbon dating, and so forth. It describes the underlying principles of radiation measurement and the detectors used. It also covers the sources of background, analyzes their effect on the detector and discusses economic ways to reduce the background. The most important types of low-level counting systems and the measurement of some of the more important radioisotopes are described here. In cases where more than one type can be used, the selection of the most suitable system is shown.