In this dissertation we describe two separate research projects. The first project involves the utilization and development of reddening models, color magnitude diagrams (CMDs), and microlensing population models of the Large Magellanic Cloud (LMC) to constrain the locations of micro-lensing source stars and micro-lensing objects in the Large Magellanic Cloud and the Milky Way (MW) halo using data of 13 microlensing source stars obtained by the MACHO (massive compact halo objects) collaboration with the Hubble Space Telescope. This analysis suggests that the source stars are located in the LMC disk and the lenses are located in the MW halo. For the second project, we report on the results of a Markov Chain Monte Carlo (MCMC) analysis of an inverse power law (IPL) quintessence model using the Dark Energy Task Force (DETF) simulated data models as a representation of future dark energy experiments. Simulated data sets were generated for a Lambda cold dark matter (ΛCDM ) background cosmology as well as a case where the dark energy is provided by a specific IPL fiducial model. The results are presented in the form of error contours generated by these two background cosmologies which are then used to consider the effects of future dark energy projects on IPL scalar field models and are able to demonstrate the power of DETF Stage 4 data sets in the context of the IPL model. We find that the respective increase in constraining power with higher quality data sets produced by our analysis gives results that are broadly consistent with the DETF results for the w₀–w_a parameterization of dark energy. Finally, using our simulated data sets constructed around a fiducial IPL model, we find that for a universe containing dark energy described by such a scalar field, a cosmological constant can be excluded by Stage 4 data at the 3σ level.