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Like Igni, Aard is so powerful that you will probably start to feel embarrassed at using it. The basic use of Aard is to set up a target for an instant kill. If it is knocked down but not Stunned or Knocked Down long enough for a finishing move, try again later when it is weaker. Typically if you have improved Aard and further enhanced it with a Ritual of Magic, it will Stun the toughest non-boss monsters up till late Chapter 5, unless they are outright immune to Aard (such as Ifrits).
The power-up version increases the effective radius and the Intensity of the Sign, which can make the difference between success or failure, but it is slow to cast. You would probably be better off burning everyone with Igni and then casting a regular Aard on the weakened target you had in mind. I recommend you skip all the power-up versions (Student, Apprentice, Specialist, Expert, Master) and work on improving Igni instead.
Blasting Fist is obviously specific to the level 4 Strong Silver style, and unless you plan on actively using that skill, skip it.
Once you hit late Chapter 5, the mini-bosses and bosses have too much protection to use Aard for anything more than getting space (by knocking enemies back -- duration of the knockdown is too short for a finishing move) or getting in safe hits (by knocking enemies down or into a wall so you can attack while they get up). At that point, Igni takes over as your main damage-dealer.