Links back to my Ezreal guide here:
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The Melancholy Of Haruhi Suzumiya is about a high school student (for Ezreal's sake, why does [almost] every anime have high school invovled?) named Haruhi Suzumiya. She's a quirky girl who does her hair about 49 different ways, gets straight A+'s, and absolutely can't stand anything "ordinary".

To brighten up her boring old Japanese high school curriculum she starts her own club called the "SOS Brigade" whose purpose is to "find and investigate all things deemed mysterious, unanswerable, incomprehensible and unfathomable." So with Haruhi Suzumiya, there is also a guy named "Kyon", a completely ordinary human being, also the narrator...

Then, there is Yuki Nagato, who is an exceptionally quiet girl who reads too much. Next, Mikuru Asahina, who is an exceptionally phlegmatic and apparently well-endowed (I wouldn't really be an expert on the subject) girl with barely a will of her own. & Finally, Itsuki Koizumi, who is this exceptionally mysterious guy...and such.

Together, the five of them go on insane adventures to alternate spaces, times, and dimensions!...Or'd have to watch it to understand...and even then there is no guarantee.

There really isn't too much I can say without spoilers. Sorry.

Anyway, it is definitely an anime for those that want something "out there" and largely original. Definitely not for people new to the medium...

The [Actual] First Episode, In Japanese (with English captions):