  We present high-precision timing data over time spans of up to 11 years for
45 millisecond pulsars observed as part of the North American Nanohertz
Observatory for Gravitational Waves (NANOGrav) project, aimed at detecting and
characterizing low-frequency gravitational waves. The pulsars were observed
with the Arecibo Observatory and/or the Green Bank Telescope at frequencies
ranging from 327 MHz to 2.3 GHz. Most pulsars were observed with approximately
monthly cadence, with six high--timing-precision pulsars observed weekly, and
all were observed at widely separated frequencies at each observing epoch in
order to fit for time-variable dispersion delays. We describe our methods for
data processing, time-of-arrival (TOA) calculation, and the implementation of a
new, automated method for removing outlier TOAs. We fit a timing model for each
pulsar that includes spin, astrometric, and, if necessary, binary parameters,
in addition to time-variable dispersion delays and parameters that quantify
pulse-profile evolution with frequency. The new timing solutions provide three
new parallax measurements, two new Shapiro delay measurements, and two new
measurements of large orbital-period variations. We fit models that
characterize sources of noise for each pulsar. We find that 11 pulsars show
significant red noise, with generally smaller spectral indices than typically
measured for non-recycled pulsars, possibly suggesting a different origin.
Future papers will use these data to constrain or detect the signatures of
gravitational-wave signals.
