We use basic results from shape theory to investigate inverse systems of
covers and the corresponding fundamental pro-groups. Many of the standard
shape-theoretic definitions become simpler in the context of covering systems
and filtered groups, and we develop the theory largely within this context. We
give several applications, including a classification of maps between P-adic
solenoids up to homotopy. Also, we develop a description of the group of
homotopy self-equivalences for certain aspherical solenoids expanding on
results of Odden and Gendron regarding the universal hypebolic solenoid.