Quark matter in astrophysics and cosmology

We discuss the role of quark matter in astrophysics and cosmology. The implications of the dynamics of the quark-hadron phase transition in the early universe for the element abundances from big gang nucleosynthesis and the composition of the dark matter in the universe are addressed. We discuss the possibility of deciding on an equation of state for high density matter by observing the cooling of a neutron star remnant of SN1987A. Quark matter models for the Centauros events, Cygnus X-3 cosmic ray events, high energy gamma-ray bursts and the solar neutrino problem are described.