  We analyze the ways in which the random first order phase transition (RFOT)
of the glass transition differs from the well-studied regular first order and
second order (or continuous) phase transitions. Just as is the case in the
latter two classes of phase transitions, the RFOT also exhibits universal
features. Here, we discuss these features and compare and contrast the RFOT
with other types of transitions with an emphasis on the structural glass
transition problem. An important feature of the complete RFOT theory is that it
has at least two distinct transition temperatures, one of which is a dynamical
(avoided) transition signaling loss of effective ergodicity, and the other is
an equilibrium ideal glass transition. Particular attention is paid to the
coherence, or correlation, length associated with these transitions in the
RFOT. We also derive universal scaling relations for several experimentally
measurable quantities that are valid near the ideal glass transition. In
particular, activated scaling ideas are used to obtain a scaling equation for
the non-linear structural glass susceptibility as the ideal glass transition is
approached. Important finite corrections to the ideal glass transition
temperature are also discussed. Our work provides additional criteria for
assessing the validity of RFOT theory of the liquid to glass transition, and
provides a firm theoretical foundation for analyzing experimental data on the
temperature dependence of the relaxation times.
