Dark matter in the Universe can be described as the matter which has practically zero luminosity and its presence can be detected only by its gravity. Historically, the first modern study of the possible presence of dark matter goes back to 1915, when Öpik (1915) determined the dynamical density of matter in our Galaxy in the Solar vicinity. The same problem was investigated by Oort (1932, 1960), Kuzmin (1952a, 1955) and more recently by Bahcall (1984) and Gilmore, Wyse & Kuijken (1989). Modern data suggest that there is little evidence for the presence of a large amount of local dark matter in the Solar vicinity. If some invisible matter is there, then it should be in the form of brown dwarfs, jupiters or similar compact baryonic objects.
A different type of dark matter is found around galaxies and in clusters of galaxies. The first evidence for the presence of such global dark matter was given by Zwicky (1933) from the dynamics of galaxies in the Coma cluster. The presence of dark matter in clusters was questioned, and an alternative solution to explain large velocities of galaxies in clusters was suggested by Ambartsumian (1958) - the instability of clusters of galaxies. However, the evidence for the presence of invisible matter in systems of galaxies accumulated, first for our Local Group of galaxies (Kahn & Woltjer 1959), and thereafter for all giant galaxies (Einasto, Kaasik & Saar 1974, Ostriker, Peebles & Yahil 1974). These results were questioned by Burbidge (1975), Materne & Tammann (1976). Independent determination of rotation velocities of galaxies at large galactocentric distances (Rubin, Ford & Thonnard 1978, 1980) confirmed previous results on the presence of dark halos or coronas around galaxies. The nature of dark matter around galaxies is not clear. Initially it was assumed that it consists of hot gas (Kahn & Woltjer 1959, Einasto 1974b). Modern data favour the hypothesis that dark matter around galaxies is non-baryonic, either neutrinos or some weakly interacting massive particles, such as axions. The neutrino-dominated dark matter is called hot, since neutrinos move with very high velocities. The other type of dark matter is called cold, as particle velocities are moderate. The cosmological model with cold dark matter (CDM) was suggested by Blumenthal et al. (1984). This model is presently accepted as the standard. With the establishment of the cold dark matter concept the early period of the study of dark matter was completed.
Excellent reviews of the dark matter problem have been given by Faber & Gallagher (1979), Trimble (1987), Turner (1991) and Silk (1992), alternatives to dark matter have been discussed by Sanders (1990). In this report I describe how astronomers developed step-by-step the concept of dark matter. Such process is typical for the formation of a new paradigm in our understanding of the Universe. Particular attention is given to the work on galactic modelling which has lead us to the understanding of the structure of stellar populations and the need for a new invisible population of dark matter in galaxies. The Power-Point version of the present report is available on the web-site of Tartu Observatory, http://www.aai.ee/~einasto.