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Sortiliena Serlut (ソルティリーナ・セルルト)Sortiliena Serlut is the mentor of Kirito during his 1st year in the North Centoria Imperial Sword Mastery Academy, and the 2nd-seat elite swordswoman at the Academy where she is known as the "Walking Tactics Manual."
She has very long straight hair and can easily be considered beautiful. As an elite-swordswoman, she customized her uniform to a purple one.
(Source: Sword Art Online Wiki)