The Large Magellanic Cloud (LMC) is one of the Milky Way's most prominent dwarf galaxy satellites. Positioned within the Milky Way's gravitational influence, the LMC offers a unique opportunity to explore near-field cosmology in the context of stellar evolution, star formation, interstellar medium behaviour, and galaxy evolution. This thesis presents detailed abundance measurements for various elements in stars within the LMC, shedding light on their chemical composition and evolution. The first study examines the presence of multiple populations in the 1.95 Gyr old LMC star cluster NGC 1846, testing the 2 Gyr boundary for clusters showing chemical abundance spread. Findings indicate no intrinsic star-to-star spread in Na and O, but significant carbon spread suggests evolutionary mixing in the red giant branch, enhancing our understanding of the existence of multiple populations in intermediate-age massive star clusters in galaxies. The second study presents a search for extremely metal-poor (EMP) stars in the LMC, crucial for unraveling the earliest stars and conditions during initial star formation in dwarf galaxies. Using SkyMapper DR3 and Gaia DR2 data, seven stars with [Fe/H] <= -2.75, including two with [Fe/H] <= -3, were found. The third study then unveiled detailed abundance results for these stars, confirming them as the most metal-poor stars known in the Magellanic Clouds. While their abundance ratios resemble Milky Way halo stars, only the more metal-rich stars display r-process element enhancements, hinting at a 100 Myr timescale for substantial r-process enrichments. Together, these studies contribute valuable insights into the chemical composition, evolutionary history, and early star formation processes within the LMC, advancing our understanding of stellar and galactic evolution.