  When a solenoid is embedded in three space, its complement is an open three
manifold. We discuss the geometry and fundamental groups of such manifolds, and
show that the complements of different solenoids (arising from different
inverse limits) have different fundamental groups. Embeddings of the same
solenoid can give different groups; in particular, the nicest embeddings are
unknotted at each level, and give an Abelian fundamental group, while other
embeddings have non-Abelian groups. We show using geometry that every solenoid
has uncountably many embeddings with non-homeomorphic complements.
