The two-dimensional (2D) phases of fatty-acid monolayers (hexadecanoic, octadecanoic, eicosanoic, and docosanoic acids) have been studied at the interface of a nematic liquid crystal (LC) and water. When observed between crossed polarizers, the LC responds to monolayer structure owing to mesoscopic alignment of the LC by the adsorbed molecules. Similar to Langmuir monolayers at the air/water interface, the adsorbed monolayer at the nematic/water interface displays distinct thermodynamic phases. Observed are a 2D gas, isotropic liquid, and two condensed mesophases, each with a characteristic anchoring of the LC zenithal tilt and azimuth. By varying the monolayer temperature and surface concentration we observe reversible first-order phase transitions from vapor to liquid and from liquid to condensed. A temperature-dependent transition between two condensed phases appears to be a reversible swiveling transition in the tilt azimuth of the monolayer. Similar to monolayers at the air/water interface, the temperature of the gas/liquid/condensed triple-point temperature increased by about 10 degrees C for a two methylene group increase in chain length. However, the absolute value of the triple-point temperatures are depressed by about 40 degrees C compared to those of analogous monolayers at the air/water interface. We also observe a direct influence by the LC layer on the mesoscopic and macroscopic structure of the monolayer by analyzing the shapes and internal textures of gas domains in coexistence with a 2D liquid. An effective anisotropic line tension arises from elastic forces owing to deformation of the nematic director across phase boundaries. This results in the deformation of the domain from circular to elongated, with a distinct singularity. The LC elastic energy also gives rise to transition zones displaying mesoscopic realignment of the director tilt or azimuth between adjacent regions with a sudden change in anchoring.