A comprehensive investigation of counters and counting circuits was initiated for the purpose of developing counters with ultimate sensitivity and capable of meeting the requirements of high speed counting. The counting process is discussed, the construction and preparation of counter are explained, and methods of obtaining high resolution and sensitivity are given. A description is given of the most important circuits for counting, and the conditions under which they are employed. The investigation resulted in new designs for gamma ray and hard X-ray counters having quantum counting efficiencies up to 50. Soft X-ray counting efficiencies of 100 were obtained. A new principle of counter construction resulted in resolving powers up to 100,000 random counts per second, as compared with the previous maximum of 3000.