"Fuzzy logic" is a fashionable term, slightly suspicious for some people. The lecture will show that fuzzy logic has a sound formal basis and should be taken seriously, not first for its large applicational success (which has to be explained) but because fuzzy logic indeed can be considered as a formal symbolic system with foundations as good as those for Boolean logic. The basic distinction, which will be repeatedly stressed, is that fuzziness concerns vagueness, impreciseness etc. but not uncertainty as probability or degree of belief. The lecture will present elements of Lukasiewicz's infinite-valued propositional and predicate logic and fuzzy theories over it as a main technical device.