AbstractInthisintroductorychapterthetopicofthebookisexplained:distinguishing valid patterns of reasoning from invalid ones. The validity may depend on the meaningofconnectiveslike‘if...,then...’,‘and’,‘or’and‘not’,inwhichcase one speaks of propositional logic. But the validity may also depend on the meaning of the quanti?ers ‘for all’ and ‘for some’, in which case one speaks of predicate logic.Ifweextendthelogicallanguagewithsymbolsforadditionandmultiplication of natural numbers, G¨odel’s famous incompleteness theorems show up. In order to have meaning, logical formulae presuppose a universe of discourse, or a set, which may be ?nite or in?nite.