Planning is a challenging research area since the early days of Artificial Intelligence. The planning problem is the task of finding a sequence of actions leading an agent from a given initial state to a desired goal state. Whereas classical planning adopts restricting assumptions such as complete knowledge about the initial state and deterministic action effects, in real world scenarios we often have to face incomplete knowledge and non-determinism. Classical planning languages and algorithms do not take these facts into account. So, there is a strong need for formal languages describing such non-classical planning problems on the one hand and for (declarative) methods for solving these problems on the other hand.In this thesis, we present the action language Kc, which is based on flexible action languages from the knowledge representation community and extends these by useful concepts from logic programming.We define two basic semantics for this language which reflect optimistic and secure (i.e. sceptical) plans in presence of incomplete information or nondeterminism. These basic semantics are furthermore extended to planning with action costs, where each action can have an assigned cost value. Here, we address optimal plans as well as plans which stay within a certain overall cost limit.Next, we develop efficient (i.e. polynomial) transformations from planning problems described in our language Kc to disjunctive logic programs which are then evaluated under the so-called Answer Set Semantics. In this context, we introduce a general new method for problem solving in Answer Set Programming (ASP) which takes the genuine "guess and check" paradigm in ASP into account and allows us to integrate separate "guess" and "check" programs into a single logic program. Based on these methods, we have implemented the planning system DLVK. We discuss problem solving and knowledge representation in Kc using DLVK by means of several examples. The proposed methods and the DLVK system are also evaluated experimentally and compared against related approaches. Finally, we present a practical application scenario from the area of design and monitoring of multi-agent systems. As we will see, this monitoring approach is not restricted to our particular formalism. / Austrian Science Funds (FWF)