This thesis is based on [5], which is joint work with David Schrittesserand Asger Tornquist. We study the notion of J -MAD families where Jis a Borel ideal on !. We show that if J is an arbitrary F ideal,or is any nite or countably iterated Fubini product of F ideals, thenthere are no analytic innite J -MAD families; and assuming ProjectiveDeterminacy there are no innite projective J -MAD families; and underthe full Axiom of Determinacy + V LpRq there are no innite J -madfamilies. These results apply in particular when J is the ideal of nitesets Fin, which corresponds to the classical notion of MAD families. Theproofs combine ideas from invariant descriptive set theory and forcing