  The random first-order transition (RFOT) theory of the structural glass
transition is reviewed in a pedagogical fashion. The rigidity that emerges in
crystals and glassy liquids is of the same fundamental origin. In both cases,
it corresponds with a breaking of the translational symmetry; analogies with
freezing transitions in spin systems can also be made. The common aspect of
these seemingly distinct phenomena is a spontaneous emergence of the molecular
field, a venerable and well-understood concept. In crucial distinction from
periodic crystallisation, the free energy landscape of a glassy liquid is
vastly degenerate, which gives rise to new length and time scales while
rendering the emergence of rigidity gradual. We obviate the standard notion
that to be mechanically stable a structure must be essentially unique; instead,
we show that bulk degeneracy is perfectly allowed but should not exceed a
certain value. The present microscopic description thus explains both
crystallisation and the emergence of the landscape regime followed by
vitrification in a unified, thermodynamics-rooted fashion. The article contains
a self-contained exposition of the basics of the classical density functional
theory and liquid theory, which are subsequently used to quantitatively
estimate, without using adjustable parameters, the key attributes of glassy
liquids, viz., the relaxation barriers, glass transition temperature, and
cooperativity size. These results are then used to quantitatively discuss many
diverse glassy phenomena, including: the intrinsic connection between the
excess liquid entropy and relaxation rates, the non-Arrhenius temperature
dependence of $\alpha$-relaxation, the dynamic heterogeneity, ... (see Comments
for the remainder of Abstract.)
