  We discuss theories of gravity with independent metric (or frame field) and
connection, from the point of view of effective field theory. We count the
parity-even Lagrangian terms of dimension up to four and give explicit bases
for the independent terms that contribute to the two-point function. We then
give the decomposition of the linearized action on a complete basis of spin
projectors and consider various subclasses of Metric-Affine Gravity theories
(MAGs). We show that teleparallel theories can be dynamically equivalent to any
metric theory of gravity and give the particle content of those whose
Lagrangian contains only dimension-two terms. We point out the existence of a
class of MAGs whose EOMs do not admit propagating degrees of freedoms. Finally,
we construct simple MAGs that contain only a massless graviton and a state of
spin/parity $2^-$ or $3^-$. As a side result, we write the relativistic wave
equation for a spin/parity $2^-$ state.
