One of the most outstanding discoveries of modern astronomy and astrophysics has been that our Universe seems to be made of materials in a form that we cannot see. We are not certain what form most of the Universe takes. It is called dark matter and we do not know its nature. This problem was first recognized by measurement of velocities of galaxies suggesting that total mass seems one order of magnitude larger than the sum of the visible masses within the galaxies themselves. Now many improved measurements showed evidences convincing that the mass density of the Universe must be greater than 10 % of the critical density -- the threshold density to discriminate close Universe and open Universe -- while the amount of matter present in the visible parts of galaxies amounts to be roughly only 1 %. In addition, theoretical favorites in terms of modern cosmology is that mass density of the Universe might exactly have the value of the critical density.

The dark matter would also resolve the basic problem of galaxy formation. The COBE measurement showed that the cosmic microwave background radiation is remarkably isotropic and smooth. Its fluctuations are too small to to form the structure of the Universe we are observing: Galaxies and clusters of galaxies. Original matter was very strongly coupled to the radiation when the Universe was very hot and this made it very difficult for the original matter to collapse to form galaxies and clusters of galaxies. If the dark matter did not interact with the original matter or the radiation, density perturbations in the dark matter could develop to larger density contrasts and the structures of the Universe can be formed without any initial non uniformity of the original matter or the radiation.

It has been claimed that pure cold dark matter (CDM) leads to a larger baryon fraction ($\Omega_{b}$) than predicted by big bang nucleosynthesis (BBN) if the observed hot X-ray-emitting gas represents a fair sample of the universe.

An admixture of hot dark matter (HDM) with CDM shifts the estimates of the baryon fraction closer to that by BBN. In addition, this mixed cold + hot dark matter model (CHDM) has been shown to agree well with the cosmic microwave background (CMB) spectrum measured by COBE, and galaxy group properties such as the number density of clusters.

Neutrinos are the best candidate for HDM and a total neutrino mass of 5 eV may be a solution consistent with all available observations.