The Self Organized Mapping (SOM) is a kind of artificial neural network (ANN) which enables the pattern set self-organization in space with Euclidean metrics. Thus, the traditional SOM consists of two layers; input one with n nodes and output one with H ones. Every output node is characterized by its weight vector Wk G in this case. The absence of pattern coordinates in special cases is a good motivation for self-organization in any metric space (U, d). The learning in the metric space is introduced on the cluster analysis problém and a basic clustering algorithm is obtained. The relationship with the traditional ISODATA method and NP-completeness is proven. The direct generalization comes to SOM learning in the metric space, its algorithm, properties and NP-completeness. The SOM learning is based on an objective function and its batch minimization. Three estimates of the proposed objective function are included. They will help to study the relationship with Kohonen batch learning, the cluster analysis and the convex programming task. The Matlab source code for the SOM in the metric space is available in the appendix. Two numeric examples are oriented at self-organization in the metric space of written words and the metric space of functions.