  Sect 1 introduces Nielsen classes attached to (G,C), where C is r conjugacy
classes in a finite group G, and a braid action on them. These give reduced
Hurwitz spaces, denoted H(G,C)^rd. The section concludes with a braid formula
for the genus of these spaces when r = 4.
  If there is at least one prime l for which G is divisible by l, but has no
Z/l quotient, then there is a canonical tower of reduced Hurwitz spaces over
H(G,C)^rd, using the Universal Frattini cover, ~G, of G, and ~G_ab, its
abelianized version. The towers are nonempty assuming C are l' classes
satisfying a cohomological condition from a lift invariant. A M(odular)T(ower)
is a projective sequence of components of the canonical tower.
  Sect 2 introduces the book [Fr18], which takes on generalizing Serre's
O(pen)I(mage)T(heorem}, interpreted as the case when G is a dihedral group D_l
and C is four repetitions of the involution conjugacy class. Serre's Theorem
separated decomposition groups of projective sequences of points in the modular
curve towers into two types: CM (complex multiplication) and GL_2. When r = 4,
all MT levels are upper half-plane quotients ramified at 0 (of order 3), 1 (of
order 2) and \infty (corresponding to the cusps). They are appropriate
therefore to compare Serre's OIT with the cusps and decomposition group fibers.
[Fr18] emphasizes new phenomena in cusps, and components, while still showing
in high tower levels a valid comparison with modular curves.
  It also aims to show how MTs can expand the applications usual for modular
curve towers, recognizing those problems directly interpret from the Inverse
Galois Problem. The l-adic representations of the title come from the
abelianized version of the Universal Frattini cover.
