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This book, the first of two volumes, provides novel perspectives on the study of abduction, by analyzing both Magnani's ample investigation of the subject and discussing its rising importance in today's epistemology and philosophy of science. Notwithstanding the long history of the concept, which has been studied since its analysis in Aristotle's Organon, in the last fifty years, it has known a resurgent interest in the epistemological literature since it is an ampliative inference deemed to be at the core of creative leaps and acts of discovery. For these reasons, different open questions still bother interested researchers: which constraints affect abductive reasoning when a hypothesis is evaluated or selected? Should we adopt a unified view on abduction or maintain a pluralistic perspective regarding its forms and functions? What kinds of models can be used in abductive reasoning? This last question, in particular, shows how the topics of the two parts of the volume are intrinsically connected and ensures they are of great importance to those interested in epistemology, philosophy of science, mathematical logic and AI.