Entanglement is one of the most fascinating features of quantum information. In this lecture the focus is on two aspects of the broad field of entanglement theory: first, on methods for the detection or verification of entanglement. Here, the method of Bell inequalities is compared with the tool of witness operators and their local measurement. An overview of other methods such as entropic and uncertainty relations, as well as physical approximations of unphysical maps, will be given. Second, the zoo of multipartite entangled states will be visited, mainly with respect to their usefulness as a resource for a given task. As an example, distributed dense coding is presented.

As a connection between the two main topics, the detection of multipartite entangled states is discussed.