This book contains the basic information about topology, category and frames then the main parts of this book are related to study of generalized nearness, generalized convergence and generalized bornology and also in their properties presented within the realm of categorical topology. In addition corresponding concepts studied on Boolean frames. The existing treatise maybe also serve as an overview of fundamental concepts, which in the past have been raising up inside the branches of general topology, set theoretic topology or categorical topology, respectively.