Sriharsha, RamThis thesis is devoted to certain aspects of string compactifications to two and three dimensions. We construct vacua that describe the propagation of non-critical strings on a singular Spin(7) space. We also examine compactifications which preserve six supercharges, and obtain the classical and quantum moduli space of such theories. We also consider compactifications on T^8/Z_2 and point out the relevance of these flux compactifications to understanding the mathematical result of Guan and Beauville on the Hodge numbers of hyperkahler four-folds.en-USDissertationPhysics, TheoryPhysics, Elementary Particles and High EnergySpin(7)hyperkahlerflux compactificationsnoncritical stringsW symmetries