Polymeric membrane gas separation technology is increasingly common in chemical industries such as natural gas purification, syngas and ammonia production, as well as air separation, and carbon dioxide capture, impacting both energy and environment. An ideal polymer membrane should have desirable gas permeability for the gas of interest, i.e. H2, O2, or CO2, and high selectivity relative to other gases such as CH4 and N2. Additionally, membrane's stability and durability under various operating conditions are of equal importance for practical implementation.Several important challenges exist for polymer gas separation membranes. The most well-known issue is the permeability-selectivity trade-off relationship, which is visualized as Robeson's upper bound. Many academic and industrial research groups have been focusing on sophisticated macromolecular design to achieve maximized permeability/selectivity combinations over the last few decades, some of which demonstrated excellent gas separation performance for multiple gas pairs, exceeding Robeson's permeability-selectivity trade-off upper bound. Even so, it has been observed that the significant improvement in permeabilities does not necessarily facilitate the improvement of selectivity, suggesting that these new polymeric membranes are still challenged by the permeability-selectivity tradeoff. Other challenges associated with polymeric gas separation membranes are physical aging, which is caused by polymer chain or segmental relaxation leading to loss in gas permeability over time, and plasticization, which occurs when the membrane is exposed to and swollen by condensable gases such as CO2. Crosslinked polymeric membranes have been shown to be resistant toward physical aging and condensable-gas-induced plasticization. However, the much improved membrane stability upon crosslinking is frequently accompanied with greatly reduced permeability due to crosslinking-induced densification. Moreover, current crosslinking approaches are essentially random crosslinking, resulting in very complex crosslinked structures with extremely limited structure tunability that prevents fundamental structure-property relationship studies for crosslinked gas separation membranes. Based upon these considerations, this dissertation reports studies of crosslinked polymer gas separation membranes with model network structures based on triptycene-containing polybenzoxazoles (TPBOs) prepared via a fundamentally new end-linking approach. In this new approach, crosslinking reaction only occurs at the chain ends of telechelic oligomers, which allows for precise control of crosslink density and crosslink inhomogeneity (i.e., uneven distribution of crosslink sites), a previously unexplored structure parameter in crosslinked membranes. The research in this thesis focused on probing the effect of various structural and fabrication parameters on membrane properties, infrastructure, and gas separation performances, including crosslinking thermal protocols, crosslinking chemistry, crosslink density, and crosslink inhomogeneity. All crosslinked model network membranes in the study displayed excellent gas separation performances compared with previously reported similar materials, suggesting their promising potential in crucial industrial gas separation and carbon capture technologies.