The word “TENSOR” in this project is understood as a multidimensional linear array of a rectangular shape, whose entries are either real or complex numbers. Such data structures are encountered, e.g., in chemometrics, telecommunication, biomedicine (fMRI, EEG) , data mining, kinetic theory of descriptions of materials, and so on. Canonical polyadic (CP) decomposition is a decomposition of a tensor to a fixed number of simpler tensors that are outer products of vectors. It is also known under the names CANDECOMP (Canonical Decomposition) of PARAFAC (Parallel Factor Analysis). It can be considered as a generalization of the factor analysis to higher dimensions. The aim of the project is to contribute to the theory of CP decomposition, design new efficient algorithms for this decomposition, and more complex tensor decompositions, and prove usefulness of these decompositions in applications such as modelling uncertainty in complex systems, blind source separation, signal classification, and clustering.