In this book, the notion of noncompact covering properties, viz., metacompactness, subparacompactness, submetacompactness and para-Lindelofness in L-topological spaces are introduced using quasi coincidence relation and a-Q-covers. Moreover the characterizations of these properties in the weakly induced L-topological spaces are obtained. Further the invariance of these properties under various kinds of fuzzy maps is also studied. Some brief sketches regarding the related topics covering dimension and finitistic spaces in L-topological spaces is also provided.