  We present updated analyses of pulse profiles and their arrival-times from
PSR B1534+12, a 37.9-ms radio pulsar in orbit with another neutron star. A
high-precision timing model is derived from twenty-two years of timing data,
and accounts for all astrophysical processes that systematically affect pulse
arrival-times. Five "post-Keplerian" parameters are measured that represent
relativistic corrections to the standard Keplerian quantities of the pulsar's
binary orbit. These relativistic parameters are then used to test general
relativity by comparing the measurements with their predicted values. We
conclude that relativity theory is confirmed to within 0.17% of its
predictions. Furthermore, we derive the following astrophysical results from
our timing analysis: a distance of $d_{\rm GR} = 1.051 \pm 0.005$ kpc to the
pulsar-binary system, by relating the "excess" orbital decay to Galactic
parameters; evidence for pulse "jitter" in PSR B1534+12 due to short-term
magnetospheric activity; and evolution in pulse-dispersion properties. As a
secondary study, we also present several analyses on pulse-structure evolution
and its connection to relativistic precession of the pulsar's spin axis. The
precession-rate measurement yields a value of $\Omega_1^{\rm spin}$ =
$0.59^{+0.12}_{-0.08}$ $^{\circ}$/year (68% confidence) that is consistent with
expectations, and represents an additional test of relativistic gravity.
