  An elementary introduction is given to the problem of black hole entropy as
formulated by Bekenstein and Hawking, based on the so-called Laws of Black Hole
Mechanics. Wheeler's `It from Bit' picture is presented as an explanation of
plausibility of the Bekenstein-Hawking Area Law. A variant of this picture that
takes better account of the symmetries of general relativity is shown to yield
corrections to the Area Law that are logarithmic in the horizon area, with a
finite, fixed coefficient. The Holographic hypothesis, tacitly assumed in the
above considerations, is briefly described and the beginnings of a general
proof of the hypothesis is sketched, within an approach to quantum gravitation
which is non-perturbative in nature, namely Non-perturbative Quantum General
Relativity (also known as Quantum Geometry). The holographic entropy bound is
shown to be somewhat tightened due to the corrections obtained earlier. A brief
summary of Quantum Geometry approach is included, with a sketch of a
demonstration that precisely the log area corrections obtained from the variant
of the It from Bit picture adopted earlier emerges for the entropy of generic
black holes within this formalism.
