The necessity of facing up to the problem of catastrophic gravitational collapse in astrophysics was first appreciated by Chandrasekhar in 1931 when he discovered the upper mass limit for a spherical equilibrium configuration of a cold sphere of ordinary degenerate matter in Newtonian gravitational theory. Subsequent work by Chandrasekhar, Landau, Oppenheimer and others established fairly clearly by the end of the nineteen thirties that the upper mass limit would not be greatly affected by taking into account the existence of exotic forms of high density matter, such as a degenerate neutron fluid, nor by the corrections resulting from the use of Einstein's theory of gravity, according to which an object above this limit must ultimately disappear from sight within its Schwarzschild horizon—which occurs when the circumferential radius r is diminished to twice the conserved mass M (where here, as throughout this work, we use units in which Newton's constant G and the speed of light c are set equal to unity)-with the subsequent formation of a singularity.