Fifteen papers presented at the workshop Data Depth: Robust Multivariate Analysis, Computational Geometry and Applications (held in May 2003 at the Rutgers University) are collected in this book. The recent development of data depth and its applications are presented by leading researchers in the field. Contributions may be divided into three main groups. Statistical theory and applications of data depth comprise the first part of the book. Among the main topics the reader will find are a general study of depth functions, tests based on data depth, development of zonoid, simplicial and spherical depth, classification and discrimination based on the depth function, regression depth and depth for functional data. The second section of presentations covers computational problems related to data depth. The main problem is to find fast algorithms for computing the depth, a process which is typically very slow, in particular in higher dimensions. The last section of contributions is devoted to geometric aspects of statistical data depth. The book can be recommended to researchers or students interested in multivariate statistical analysis and its applications.