The advanced open water diver course offered by PADI is a little misleading by its name. It is not an advanced course per say although rather a course that you take after your open water certification to advance your diving skills.
I would highly recommend this course to anyone and would suggest completing it as soon as possible after your open water. I suggest this for three reasons, its a lot of fun, it provides more time with a dive professional and gives you the opportunity to hone your skills.
In some ways it can be more enjoyable that the open water course as there is less of an emphasis on skills and more on diving. PADI would prefer you to first complete what they call adventures in diving, but really those are just a subset of this course, so again I would recommend getting straight into it.
With the advanced open water diver course you choose five specialties that your would like to learn more about, here is a list of possible choices:
Altitude Adventure Dive
AWARE – Fish Identification Adventure Dive
AWARE – Shark Conservation Adventure Dive
Boat Adventure Dive
Deep Adventure Dive (M)
Digital Underwater Photography Adventure Dive
Diver Propulsion Vehicle (DPV) Adventure Dive
Drift Adventure Dive
Dry Suit Adventure Dive
Enriched Air Adventure Dive (R)
Multilevel and Computer Adventure Dive
Night Adventure Dive (R)
Peak Performance Buoyancy Adventure Dive (R)
Search and Recovery Adventure Dive
Sidemount Adventure Dive
Underwater Naturalist Adventure Dive
Underwater Navigation Adventure Dive (M)
Underwater Photography Adventure Dive
Underwater Videography Adventure Dive
Wreck Adventure Dive
As you can see there are a few to choose from and depending on where you are diving may dictate what is possible, for if you are in the tropics you may struggle asking to do an altitude dive.
From the list, there are two dives that are mandatory, Deep and Navigation, marked (M). This means that you have three to choose. Its up to you what you would like to try, although I suggest enriched air or Nitrox, Night and Buoyancy. I suggest these for the following reasons. Using Nitrox will enhance your diving, you will have extended bottom times and theoretically reduce the risk of DCI. Night as this is an amazing experience, something like you have never done before and finally Buoyancy as this will help you perfect your in water trim, which will make your dives more enjoyable and help to protect the environment.