Crush on my academic advisor.

You haven't yet flirted with her (or made any reference to such), and yet you are projecting being in a RELATIONSHIP.. slow down there trigger. Putting excess importance on getting the girl, before you know anything about her could be a path to disappointment.

Does she have a boyfriend?

Is there a conflict with dating an Advisor? ..does she grade your work or anything? ..is it allowed?

Indirect Game can safeguard you against an awkward situation in this case. You could be direct and confident and say, "I like you.. would we get into trouble if we had a coffee rendezvous?" If she already likes you for any reason, your physical looks.. your personality.. or anything else.. AND she's not in a serious relationship.. AND it's allowed by the university.. THEN a direct approach would work. If those things are true and it's not allowed by the university then it still might work.

If you are direct, and she's not already attracted to you.. but she is neutral.. then if you are just confident in the right way, and you transition and tease a little to create sexual tension between both of you.. then that might work also.. as long as those other factors are not an issue. BUT.. by being direct you give the game away, and if you are not yet very confident with women you might put yourself in a situation where it becomes uncomfortable between you and an advisor.

Being Indirect, you are just being interesting in the right way, and when done right you are being a guy that women find attractive.. but as far as she knows you just see her in a platonic light.. as far as she knows she is the one that has to convey her interest in you once she realises that she is attracted to you. When not giving the game away you can convey confidence.. you may tease her a little with but a mere hint at any kind of flirtation.. SHE has to make the first move. Not necessarily a move, but demonstration of interest.. then you can safely pickup on that interest and be more direct.

Considering this is all new to you, I advise that you use discretion. How to move forwards should be your own judgement. Perhaps when "practising" you would be better to meet women under different less complicated circumstances.

You are effectively asking the whole age question here again. So perhaps we should discuss that. It's absolutely fine to like older women. I wrote in another post how I find some 40 year old women extremely attractive. Many women like younger guys, some are not open to younger guys. If you are good with women and it's not an issue to YOU.. then it will be far less important to THEM.