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We study two different types of (maximal) almost disjoint families: very madfamilies and (maximal) cofinitary groups. For the very mad families we provethe basic existence results. We prove that MA implies there exist many pairwiseorthogonal families, and that CH implies that for any very mad family there isone orthogonal to it. Finally we prove that the axiom of constructibilityimplies that there exists a coanalytic very mad family. Cofinitary groups havea natural action on the natural numbers. We prove that a maximal cofinitarygroup cannot have infinitely many orbits under this action, but can have anycombination of any finite number of finite orbits and any finite (but nonzero)number of infinite orbits.  We also prove that there exists a maximal cofinitary group into which eachcountable group embeds. This gives an example of a maximal cofinitary groupthat is not a free group. We start the investigation into which groups havecofinitary actions. The main result there is that it is consistent that$\bigoplus_{\alpha \in \aleph_1} \mathbb{Z}_2$ has a cofinitary action.  Concerning the complexity of maximal cofinitary groups we prove that theycannot be $K_\sigma$, but that the axiom of constructibility implies that thereexists a coanalytic maximal cofinitary group. We prove that the leastcardinality $\mathfrak{a}_g$ of a maximal cofinitary group can consistently beless than the cofinality of the symmetric group. Finally we prove that$\mathfrak{a}_g$ can consistently be bigger than all cardinals in Cicho\'n'sdiagram.

Cofinitary Groups and Other Almost Disjoint Families of Reals