The branching fractions for tau --> e nu nu(tau), mu nu nu(tau), and h
nu(tau) are measured using data collected with the CLEO detector at t
he CESR e(+)e(-) collider: B-e = 0.1776 +/- 0.0006 +/- 0.0017, B-mu =
0.1737 +/- 0.0008 +/- 0.0018, and B-h = 0.1152 +/- 0.0005 +/- 0.0012,
where the first errors are statistical, the second systematic, and h r
efers either to a charged pi or K. Also measured is the tan mass, m(ta
u) = (1778.2 +/- 1.4) MeV. Lepton universality is affirmed by the resu
lting relative branching fractions (B-mu/B-e = 0.9777 +/- 0.0063 +/- 0
.0087, B-h/B-e = 0.6484 +/- 0.0041 +/- 0.0060) and the charged-current
gauge coupling-constant ratios (g(mu)/g(e) = 1.0026 +/- 0.0055, g(tau
)/g(mu) = 0.9990 +/- 0.0098). The tau mass result may be recast as a t
au neutrino mass limit, m(nu tau) < 60 MeV at 95% CL.