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 { u}5+3{ u}6 and 2{ u}3+2{ u}6 bands of CH3D.
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