The work reported in this thesis describes the successful preparation of three classes of polymer that were designed to possess intrinisic microporosity from a range of aromatic tetrahydroxy and diamine monomers. The tetrahydroxy family of monomers were used to prepare a number of polybenzodioxane polymers and co-polymers using the chemistry developed for the archetypal PIM-1. Two co-polymers formed films suitable for gas permeability measurements indicating that they transport gases at high selectivity but lower permeability as compared to PIM-1. The diamino-containing monomers were used to prepare a number of polyimides (PIM-PIs) using well-established polymerisation chemistry and also some Troger’s base polymers (PIMTBs) using a recently developed polymerisation method. A series of TB-PIMs with different substituents next to the amino group (H and CH3) and containing various pendant groups were prepared in order to establish structure-property relationships. Some of these polymers proved microporous with surface areas ranging from 22-510 m2/g. Unfortunately, none were suitable for film formation or gas permeation measurements. PIM-PIs were prepared from diamino monomers based on bulky 1,4-ditritylbenzene (BAB), adamantane (AD) and trifluorodiaminoaryl (TFA) units by reaction with commercial 4,4′- (hexafluoroisopropylidene)diphthalic anhydride (6FDA). Some of these polymers also demonstrated microporosity with surface areas ranging from 8-560 m2/g. Two polymers (PIM-AD5- PI and PIM-AD6-PI), exhibited good solubility, excellent thermal stability and intrinsic microporosity, with the introduction of highly rigid and bulky groups adjacent to the imide group. PIM-AD5-PI and PIM-AD6-PI demonstrate a very good combination of high permeability and good selectivity for CO2/CH4, H2/N2 and H2/CH4 gas pairs with data that lie close to the Robeson 2008 upper bounds, which is the benchmark for the evaluation of the potential of a new polymer for making gas separation membranes. Finally, a series of trifluoromethyl (CF3) containing PIM-PIs were prepared. Again, it was found that by increasing the rigidity of the polymers by increasing the number of methyl substituents a greater amount of intrinsic microporosity is generated by the polymer. Seven polymers of this series formed robust films suitable for gas permeability measurements and demonstrated good selectivity for CO2/CH4, O2/N2, H2/N2 and H2/CH4 gas pairs with data that lie near the 2008 upper bounds.