Geometric measures of quantum correlations with Bures and Hellinger distances

This article contains a survey of the geometric approach to quantum correlations. We focus mainly on the geometric measures of quantum correlations based on the Bures and quantum Hellinger distances.
Comment: to be published as a chapter of the book "Lectures on general quantum correlations and their applications" edited by F. Fanchini, D. Soares-Pinto, and G. Adesso (Springer, 2017); 47 pages, 3 figures; second version: minor typos in the first version corrected