Possible worlds models have been defined by Saul Kripke in the early 60ies. They provide semantics for various modal logics such as temporal logics, logics of knowledge and belief, logics of action, logics of obligation, as well as for description logics. They also give semantics for other nonclassical logics such as intuitionistic logics, conditional logics, and several paraconsistent and relevant logics. These logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in various domains such as program semantics, artificial intelligence, and more recently  in the semantic web. For almost all of these logics there exist semantic tableaux proof systems which for a given formula allow to check whether it has a model. The present book contains a step-by-step introduction to possible worlds semantics and modal and other nonclassical logics. It is accompanied by a piece of software that allows to build models, to check whether a given formula is true in a model, and to check whether a given formula is valid in a given logic. Beyond working with existing tableaux systems, the program also allows to implement tableau systems for new logics by means of a simple interactive graph-based language accessible to readers that are not computer scientists.