We construct an extensive set of equilibrium sequences of rotating pol
ytropes in general relativity. We determine a number of important phys
ical parameters of such stars, including maximum mass and maximum spin
rate. The stability of the configurations against quasi-radial pertur
bations is diagnosed. Two classes of evolutionary sequences of fixed r
est mass and entropy are explored: normal sequences which behave very
much like Newtonian evolutionary sequences, and supramassive sequences
which exist solely because of relativistic effects. Dissipation leadi
ng to loss of angular momentum causes a star to evolve in a quasi-stat
ionary fashion along an evolutionary sequence. Supramassive sequences
evolve towards eventual catastrophic collapse to a black hole. Prior t
o collapse, the star must spin up as it loses angular momentum, an eff
ect which may provide an observational precursor to gravitational coll
apse to a black hole.