This talk is intended to provide an introduction to the concept of Independent Component Analysis (ICA), also known as Blind Source Separation (BSS). The goal of ICA is the decomposition of a set of multi-sensor data in an a priori unknown linear mixture of a priori unknown source signals, relying on the assumption that the source signals are mutually statistically independent. We will follow an algebraic approach: in a natural way, ICA poses the question of

generalizations of matrix algebraic techniques to multilinear algebra, i.e., the algebra of ``multi-way matrices'' or ``higher-order tensors''. We will discuss four orthogonal tensor decompositions that can be interpreted as higher-order counterparts of the symmetric matrix Eigenvalue Decomposition (EVD). Like for instance the EVD and the Singular Value Decomposition (SVD) of matrices, these decompositions can be considered as tools, useful for a wide range of applications.