The study of lunar surface is of prime scientific importance as it preserves record of early geological history of the solar system. This thesis investigate the chemical composition of lunar surface through X-ray fluorescence (XRF) technique, utilizing data from the Chandrayaan-1 X-ray Spectrometer (C1XS). The C1XS on board Chandrayaan-1 was designed to map the abundances of major rock-forming elements viz., Mg, Al, Si, Ca, Ti and Fe on the lunar surface.A comprehensive summary of complete C1XS observations is reported. This thesis provides a detailed description of C1XS data selection methods and spectral analysis procedures. One of the major findings of the thesis is the demonstration of first direct detection and quantification of moderately volatile element Sodium (Na) on the lunar surface. A new XRF inversion algorithm (x2abundance) that can convert XRF line intensities to elemental abundances is detailed. Validation of x2abundance using laboratory XRF experiments and GEANT4 simulations with metal alloys and lunar analog rocks are explained in detail. The new results of abundances derived from C1XS observed regions and their comparison with other earlier observations are reported. These results clearly show enhanced Na abundances on the Moon, at a few locations. This firmly establishes the refined inversion method while enabling new capacity to impose tighter constraints on the derived elemental abundances. The discovery of enhanced Na abundances suggest a relatively cooler lunar surface evolution than expected. New insights from C1XS abundance results and its scientific implications are well described. A rationale for a future improved global elemental mapping of lunar surface and the capabilities of the CLASS experiment on board the upcoming Chandrayaan-2 mission have also been described. Swept Charge Devices (SCD) are employed in C1XS and the CLASS experiments. A detailed model to simulate photon interaction and charge propagation in SCD is developed. Development of algorithm, implementation and its usage to understand the ground calibration data of C1XS is demonstrated. This Monte Carlo simulation would be quite useful during the calibration of the CLASS instrument. At the end, new developments with a few X-ray instrumental design aspects which can potentially improve future surface exploration of the Moon/airless planetary bodies in X-rays are discussed.