  Minisuperpace Quantum Cosmology is an approach by which it is possible to
infer initial conditions for dynamical systems which can suitably represent
observable and non-observable universes. Here we discuss theories of gravity
which, from various points of view, extend Einstein's General Relativity.
Specifically, the Hamiltonian formalism for $f(R)$, $f(T)$ and $f(\mathcal{G})$
gravity, with $R$, $T$, and $\mathcal{G}$ being the curvature, torsion and
Gauss--Bonnet scalars, respectively, is developed starting from the
Arnowitt-Deser-Misner approach. The Minisuperspace Quantum Cosmology is derived
for all these models and cosmological solutions are obtained thanks to the
existence of Noether symmetries. The Hartle criterion allows the interpretation
of solutions in view of observable universes.
