ABSTRACT
This chapter provides an introduction to tensor notation and reviews physical properties and tensors. One can generalize the vector notation by the introduction of mathematical entities, tensors, which transform themselves as do the products of vectors. The number of vectors concerned defines the tensor rank. A rank 1 tensor clearly transforms itself like a single vector under a unitary transformation of the basis. A rank 2 tensor transforms itself like a product of two vectors, and the contravariant components of this tensor obey the law of transformation. The coefficients of the metric enable the transformation of the covariant and contravariant components. The derivation of a tensor changes the direction of the basis vectors and means that the derivative of a vector is no longer a vector. When an elastic environment is deformed, constraints are created and a tensor of constraints corresponds to each tensor of deformations.
