So I know this is a really old thread, but since I managed to stumble upon it in 2017 I imagine others might as well. I feel the need to weigh in on this to avoid confusing people.

In ADAD bouzouki tuning, you would tune the lowest course to the next A below the D that the 3rd course is tuned to. In other words, if you place your finger on the 5th fret of the lowest course, it should make the same note as the open 3rd course. It will be one full step higher than the G in GDAD tuning. It is a great tuning, and with a capo on the 5th it puts you in ideal Irish range and gives you great possibilities for accompanying in all the common keys in Irish trad.

Regarding David A's suggestion to tune "ADAD" with the lowest A being a full octave lower than in the normal ADAD tuning, this is not what people are talking about when they refer to ADAD tuning. Frankly, what he suggests sounds totally bonkers to me. I mean no offense and don't want to disparage people's preferences, but what David suggests is a very idiosyncratic tuning. The interval between the two lowest courses would be awkwardly large, to the point that you wouldn't really be able to play melody/bass lines between the two courses. And, of course, melodic and countermelodic accompaniment is what bouzouki does best in trad. You could use the lowest A as a sort of low drone, but if this were your intention you'd probably be better off tuning DDAD with the lowest D one octave below the next. This is because 1) the DAD tuning is better suited to playing in D than in A and 2) Irish music is far more commonly in D (and related keys) than it is in A.

Of course, you can play just fine with just the three DAD courses, like Alec Finn does. But you might as well use that extra course you paid for.

A Greek Bouzouki can, in fact, be tuned GDAD or ADAD, and Irish trad. musicians do it all the time. The key is that when you do this, you can't use the same gauge strings as you would on an Irish bouzouki since Greek bouzoukis are meant for lower tension. So your best bet would be to calculate what the total tension would be with Greek tuning, then figure out how to balance it so that your GDAD/ADAD set leaves it at around the same tension. Here's a great site for doing just this: http://www.mcdonaldstrings.com/stringxxiii.html