This chapter gives an overview of various existing formalizations of non-monotonic reasoning.1 To start with, it may be useful to derive from the previous chapter two basic motivations for using nonmonotonic forms of reasoning. The first is common to all domains of common-sense reasoning. In solving a problem people do not always have enough information to make a safe step towards the conclusion; instead, they often have to jump to conclusions by applying general, defeasible rules, since finding the information which would guarantee a safe landing is often too costly or even impossible. But instead of acting, planning or judging on an ad hoc basis or even worse, doing nothing, people still want to take their decisions in a rational way; and a general rational principle people employ is: assume as much as possible that things are normal; under this assumption conclusions can be drawn which have to be retracted only in unusual circumstances.