Clustering is the process of grouping together objects that are similar. The similarity between objects is evaluated by using a several types of dissimilarities (particularly, metrics and ultrametrics). After discussing partitions and dissimilarities, two basic mathematical concepts important for clustering, we focus on ultrametric spaces that play a vital role in hierarchical clustering. Several types of agglomerative hierarchical clustering are examined with special attention to the single-link and complete link clusterings. Among the nonhierarchical algorithms we present the k-means and the PAM algorithm. The well-known impossibility theorem of Kleinberg is included in order to illustrate the limitations of clustering algorithms. Finally, modalities of evaluating clustering quality are examined.