In recent years, the Peircean concept of abduction has been differentiated into different forms and made fruitful in a variety of contexts. However, the very notion of abduction still seems to be in need of clarification. The present contribution takes very seriously Peirce's claim (1) that there are only three kinds of reasoning, that is, abduction, deduction, and induction, and (2) that these are mutually distinct. Therefore, the fundamental features of the three inferences canvassed, in particular as regards inferential subprocesses and the validity of each kind of reasoning. It is also argued that forms of abduction have to be distinguished along two dimensions: one concerns levels of abstraction (from elementary embodied and perceptual levels to high-level scientific theorizing). The other concerns domains of reasoning such as explanatory, instrumental, and moral reasoning. Moreover, Peirce's notion of theorematic deduction is taken up and reconstructed as inverse deduction. Based on this, inverse abduction and inverse induction are introduced as complements of the ordinary forms. All in all, the contribution suggests a taxonomy of inferential reasoning, in which different forms of abduction (as well as deduction and induction) can be systematically accommodated. The chapter ends with a discussion on forms of abduction found in the current literature.