We present the first linear polarization measurements from the 2015
long-duration balloon flight of SPIDER, an experiment designed to map the
polarization of the cosmic microwave background (CMB) on degree angular scales.
Results from these measurements include maps and angular power spectra from
observations of 4.8% of the sky at 95 and 150 GHz, along with the results of
internal consistency tests on these data. While the polarized CMB anisotropy
from primordial density perturbations is the dominant signal in this region of
sky, Galactic dust emission is also detected with high significance; Galactic
synchrotron emission is found to be negligible in the SPIDER bands. We employ
two independent foreground-removal techniques in order to explore the
sensitivity of the cosmological result to the assumptions made by each. The
primary method uses a dust template derived from Planck data to subtract the
Galactic dust signal. A second approach, employing a joint analysis of SPIDER
and Planck data in the harmonic domain, assumes a modified-blackbody model for
the spectral energy distribution of the dust with no constraint on its spatial
morphology. Using a likelihood that jointly samples the template amplitude and
$r$ parameter space, we derive 95% upper limits on the primordial
tensor-to-scalar ratio from Feldman-Cousins and Bayesian constructions, finding
$r<0.11$ and $r<0.19$, respectively. Roughly half the uncertainty in $r$
derives from noise associated with the template subtraction. New data at 280
GHz from SPIDER's second flight will complement the Planck polarization maps,
providing powerful measurements of the polarized Galactic dust emission.