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This article is a survey into clustering applications and algorithms. A number of important well-known clustering methods are discussed. The authors present a brief history of the development of the field of clustering, discuss various types of clustering, and mention some of the current research directions in the field of clustering. More specifically, top-down and bottom-up hierarchical clustering are described. Additionally, K-Means and K-Medians clustering algorithms are also shown. The concept of representative points is introduced and the technique of discovering them is presented. Immense data sets in clustering often necessitate parallel computation. The authors discuss issues involving parallel clustering as well. Clustering deals with a large number of experimental results. The authors provide references to these works throughout the article. A table for comparing various clustering methods is given in the end. The authors give a summary and an extensive list of references, including some of the latest works in the field, to conclude the article.