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Topology-based methods are of increasing importance in the analysis and visualization of dataset from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. (see also below for a list of selected issues). While there is an increasing number of high-quality publications in this field,...

This book contains the best 20 peer-reviewed papers resulting from the discussions and presentations at the third workshop on "Topological Methods in Data Analysis and Visualization", held 2009 in Utah, US. It offers an important contribution to the field.