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Experimental and theoretical methods of investi gating the variations of cosmic rays (time varia tions of their intensity) are given. The ac cumulated experimental material is systematized and analyzed, and the hypotheses that have been proposed for the origin of various types of variations are critically considered. A theory is proposed for the origin of the variations, and their correlation with various geophysical and astrophysical phenomena is examined, in particular their correlation with the properties of the solar corpuscular streams and with the electro magnetic conditions in the neighborhood of the earth, in the solar atmosphere, in interplanetary space, and in the Galaxy. This work is intended for scientists occupied with cosmic-ray physics, astrophysics, geophysics, or meteorology, for students of advanced courses in these specialties, and for workers in the network of stations for continuous cosmic-ray observations. (Author).