Although many of the instruments planned for the TMT (Thirty Meter Telescope) have their own closely-coupled adaptive optics systems, TMT will also have a facility Adaptive Optics (AO) system feeding three instruments on the Nasmyth platform. For this Narrow-Field Infrared Adaptive Optics System, NFIRAOS (pronounced nefarious), the TMT project considered two architectures. One, described in this paper, employs conventional deformable mirrors with large diameters of about 300 mm and this is the reference design adopted by the TMT project. An alternative design based on MEMS was also studied, and is being presented separately in this conference. The requirements for NFIRAOS include 0.8-5 microns wavelength range, 30 arcsecond diameter output field of view (FOV), excellent sky coverage, and diffraction- limited atmospheric turbulence compensation (specified at 133 nm RMS including residual telescope and science instrument errors.) The reference design for NFIRAOS includes multiple sodium laser guide stars over a 70 arcsecond FOV, and an infrared tip/tilt/focus/astigmatism natural guide star sensor within instruments. Larger telescopes require greater deformable mirror (DM) stroke. Although initially NFIRAOS will correct a 10 arcsecond science field, it uses two deformable mirrors in series, partly to provide sufficient stroke for atmospheric correction over the 30 m telescope aperture, but mainly to partially correct a 2 arcminute diameter "technical" field to sharpen near-IR natural guide stars and improve sky coverage. The planned upgrade to full performance includes replacing the groundconjugated DM with a higher actuator density, and using a deformable telescope secondary mirror as a "woofer." NFIRAOS incorporates an instrument rotator and selection of three live instruments: a near-Infrared integral field Imaging spectrograph, a near-infrared echelle spectrograph, and after upgrading NFIRAOS to full multi-conjugation, a wide field (30 arcsecond) infrared camera.