From the perspective of black hole thermodynamics, this exposition provides the physical and mathematical account of thermodynamic geometries, higher derivative corrections, N= 1, 2, 4 configurations, Calabi-Yau compactification, string theory and M-theory. We illustrate the local and global statistical stabilities and phase transitions for an ensemble of Kerr black holes in general relativity, and thereby consider a class of macroscopic attractors, including (non)BPS black holes, (non)extremal black holes, and (non)supersymmetric black holes in supergravity theories. For a given black brane ensemble, we shed light on the limiting thermodynamic fluctuations and higher order effects by considering Sen entropy function method as a generalized attractor and its quantum counterparts via the AdS/CFT correspondence. This research gives string (field) theory and M-theory fundamentals for the state-space, chemical, Legendre transformed and short distance (quasi) geometries. From the...