  These lectures are a pedagogical -- not comprehensive -- introduction to the
applications of effective field theory in the context of nuclear and atomic
physics. A common feature of these applications is the interplay between
nonperturbative physics (needed at leading order to produce nonrelativistic
bound states and resonances) and controlled perturbative corrections (crucial
for predictive power). The essential ideas are illustrated with the simplest
nuclear EFT, Pionless EFT, which contains only contact interactions and, with
minor changes, can be adapted to certain atomic systems. This EFT exploits the
two-body unitarity limit, where renormalization leads to discrete scale
invariance in systems of three and more bodies. Remarkably complex structures
then arise from very simple leading-order interactions. Some of the challenges
and rewards of including long-range forces -- pion exchange in Chiral EFT for
nuclear systems or Van der Waals forces between atoms -- are briefly described.
