  We have obtained spatially resolved spectra of Titan in the near-infrared J,
H and K bands at a resolving power of ~5000 using the near-infrared integral
field spectrometer (NIFS) on the Gemini North 8m telescope. Using recent data
from the Cassini/Huygens mission on the atmospheric composition and surface and
aerosol properties, we develop a multiple-scattering radiative transfer model
for the Titan atmosphere. The Titan spectrum at these wavelengths is dominated
by absorption due to methane with a series of strong absorption band systems
separated by window regions where the surface of Titan can be seen. We use a
line-by-line approach to derive the methane absorption coefficients. The
methane spectrum is only accurately represented in standard line lists down to
~2.1 {\mu}m. However, by making use of recent laboratory data and modeling of
the methane spectrum we are able to construct a new line list that can be used
down to 1.3 {\mu}m. The new line list allows us to generate spectra that are a
good match to the observations at all wavelengths longer than 1.3 {\mu}m and
allow us to model regions, such as the 1.55 {\mu}m window that could not be
studied usefully with previous line lists such as HITRAN 2008. We point out the
importance of the far-wing line shape of strong methane lines in determining
the shape of the methane windows. Line shapes with Lorentzian, and
sub-Lorentzian regions are needed to match the shape of the windows, but
different shape parameters are needed for the 1.55 {\mu}m and 2 {\mu}m windows.
After the methane lines are modelled our observations are sensitive to
additional absorptions, and we use the data in the 1.55 {\mu}m region to
determine a D/H ratio of 1.77 \pm 0.20 x 10-4, and a CO mixing ratio of 50 \pm
11 ppmv. In the 2 {\mu}m window we detect absorption features that can be
identified with the {\nu}5+3{\nu}6 and 2{\nu}3+2{\nu}6 bands of CH3D.
