An algorithm solving a graph problem is usually expected to have fast random access to the input graph G and a working memory being able to store G completely. These powerful assumptions are put in question by massive graphs that exceed common working memories and that can only be stored on disks or even tapes. Here, random access is very time-consuming. To tackle massive graphs stored on external memories, the semi-streaming model has been proposed. It permits a working memory of restricted size and forbids random access to G. In contrast, the input is assumed to be a stream of edges in arbitrary order. In this book we develop algorithms in the semi-streaming model approaching different graph problems. For the problems of testing graph connectivity and bipartiteness and for the computation of a minimum spanning tree, we show how to obtain optimal running times. For the intractable problem of finding a maximum weighted matching, we present the best known approximation algorithm. Finally, we show the minimum and the maximum cut problem in a graph both to be intractable in the semi-streaming model and give algorithms that approximate respective solutions in a randomized fashion.