We study two different types of (maximal) almost disjoint families: very mad
families and (maximal) cofinitary groups. For the very mad families we prove
the basic existence results. We prove that MA implies there exist many pairwise
orthogonal families, and that CH implies that for any very mad family there is
one orthogonal to it. Finally we prove that the axiom of constructibility
implies that there exists a coanalytic very mad family. Cofinitary groups have
a natural action on the natural numbers.