We have mapped the NGC 2023 reflection nebula in [CII] and CO(11--10) with the heterodyne receiver GREAT on SOFIA and obtained slightly smaller maps in 13CO(3--2), CO(3--2), CO(4--3), CO(6--5), and CO(7--6) with APEX in Chile. We use these data to probe the morphology, kinematics, and physical conditions of the C II region, which is ionized by FUV radiation from the B2 star HD37903. The [CII] emission traces an ellipsoidal shell-like region at a position angle of ~ -50 deg, and is surrounded by a hot molecular shell. In the southeast, where the C II region expands into a dense, clumpy molecular cloud ridge, we see narrow and strong line emission from high-J CO lines, which comes from a thin, hot molecular shell surrounding the [CII] emission. The [CII] lines are broader and show photo evaporating gas flowing into the C II region. Based on the strength of the [13CII] F=2--1 line, the [CII] line appears to be somewhat optically thick over most of the nebula with an optical depth of a few. We model the physical conditions of the surrounding molecular cloud and the PDR emission using both RADEX and simple PDR models. The temperature of the CO emitting PDR shell is ~ 90 -- 120 K, with densities of 10^5 -- 10^6 cm^-3, as deduced from RADEX modeling. Our PDR modeling indicates that the PDR layer where [CII] emission dominates has somewhat lower densities, 10^4 to a few times 10^5 cm^-3
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