  In this paper, we review and extend a family of log-det divergences for
symmetric positive definite (SPD) matrices and discuss their fundamental
properties. We show how to generate from parameterized Alpha-Beta (AB) and
Gamma Log-det divergences many well known divergences, for example, the Stein's
loss, S-divergence, called also Jensen-Bregman LogDet (JBLD) divergence, the
Logdet Zero (Bhattacharryya) divergence, Affine Invariant Riemannian Metric
(AIRM) as well as some new divergences. Moreover, we establish links and
correspondences among many log-det divergences and display them on alpha-beta
plain for various set of parameters. Furthermore, this paper bridges these
divergences and shows also their links to divergences of multivariate and
multiway Gaussian distributions. Closed form formulas are derived for gamma
divergences of two multivariate Gaussian densities including as special cases
the Kullback-Leibler, Bhattacharryya, R\'enyi and Cauchy-Schwartz divergences.
Symmetrized versions of the log-det divergences are also discussed and
reviewed. A class of divergences is extended to multiway divergences for
separable covariance (precision) matrices.
