A mathematical object that may refer to many kinds of physical rotations, in particular to the rotational part in the polar decomposition of the gradient of the radius vector in the classical continuum, to the (independent) rotation of a point body in the Cosserat continuum, or to any other rotation, for instance, to the rotation of a rigid body, of a co-ordinate system etc. In the following discussion, it is an orthogonal tensor characterizing rotation of vectors and rigid bodies. If d is a vector subjected to rotation, the rotated vector equals d' = P d, where P is the rotation tensor, det P = 1. Each rotation tensor may be represented via the rotation angle and axis of rotation (theorem by Leonhard Euler): P = (1 - cos ? ) n n + cos ? I + sin? I x n, where I is the identity tensor (I d = d for each vector d), n is the axis of rotation. For linear motions, P is approximately equal to I +? n x I. In the literature, the rotation tensor is also called the turn tensor. In micropolar media, one has to distinguish the rotation of the background continuum, related to the gradient of translational deformation, and the proper rotation of particles. In linear elasticity and seismology the rotation tensor refers to a different object, and the expression for P is simplified by the infinitesimal nature of the rotation angle, not the linear motion. See Pujol (2009)