Visualization research aims at providing insights into large, complex bodies of data. Topological methods are distinguished by their solid mathematical foundation, guiding the algorithmic analysis and its presentation among the various visualization techniques. This book contains 13 peer-reviewed papers resulting from the second workshop on ''Topology-Based Methods in Visualization'', held 2007 in Grimma near Leipzig, Germany. All articles present original, unpublished work from leading experts. Together, these articles present the state of the art of topology-based visualization research.