I'm doing research on Celestia for a video and would like some assistance. Specifically this is a character study of her. An in depth analysis of what makes her tick and what could potentially be inferred about her as a character.

I suppose that depends on what you are looking for. There are different versions of Celestia. The "official" one in the Hasbro My Little Pony show, The supplemental canon version in the Hasbro My Little Pony books, The loosely canon version in the IDW My Little Pony comics, and the very vaguely canon versions in the fan fictions here on Fimfiction. What are you starting with?

well the more important thing would be her as a mentor.

She has been alone for a looong time and might get a little despite for a love life even if it maybe forbidden. We don't really know much about what makes her mad but we do know that she got mad at Chrysalis, never wants Discord around cause he acts like an overgrown child, and some of the other villains. And Twilight being stupid. Aka The Want Smarty Pants need Smarty Pants incident. She is usually the motherly type to everypony except the elements and Luna. I hope this is a good bit of info.

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I'm interested in all interpretations of her. The show I know best and I've never read the comics or the more well known fan interpretations.

I have read... 1 comic about them going to the sister hooves social.

From a comic store.

So it's legit.

Never got to the end though.

But from my Pov. She is the all powerful pony princess that wants somepony to love her and treat her like an equal not as a goddess that everypony fears. She's smart, beautiful, can sometimes be funny without realizing it, Lonely, feared, has a secret dark side, she has the biggest responsibility that most ponies couldn't handle and I respect her for that. I can't help but feel that she doesn't need her sister or Twilight but a true friend that isn't afraid of her or wants to be her friend just for boasting.

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A straightforward starting point would be her page on MLP.wikia.com. You might not necessarily agree with everything there, but it does contain useful information as a launching point for further discussion. Most useful would be the "Appearances" subsection, which makes a note of - what else? - her appearances, background cameos, and mentions in multiple episodes. That should save you some time when it comes to revisiting the series episodes for primary references.

Here you go:

http://mlp.wikia.com/wiki/Princess_Celestia#Appearances

And I hope that helps.

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What is UP, dude? I'm doin' the same damn thing. Tell me whatcha need and I will look for it!

(I'm really relaxed about what I'm doing, so I prefer helping someone else do it until I get around to doing it myself in... a year... or two...)

I know the fans tend to interpret her as a goofy mare with a ridiculous sense of humor and trolling. Or they really want Luna to overthrow her (for some reason) a la Tyrantlestia. Fics have been slowly moving more toward the canon portrayal of her, though, in which she's sweet to every pony, kind, motherly, a mentor figure to Twilight, and (seemingly) an extreme pacifist.