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This Special Issue "Differential Geometrical Theory of Statistics" collates selected invited and contributed talks presented during the conference GSI'15 on "Geometric Science of Information" which was held at the Ecole Polytechnique, Paris-Saclay Campus, France, in October 2015 (Conference web site: http://www.see.asso.fr/gsi2015).

Entropy --- Coding Theory --- Maximum entropy --- Information geometry --- Computational Information Geometry --- Hessian Geometry --- Divergence Geometry --- Information topology --- Cohomology --- Shape Space --- Statistical physics --- Thermodynamics