Daughter of the Drow (Forgotten Realms: Starlight and Shadows Book 1) by Elaine Cunningham

Liriel Baenre daughter of Gromph Baenre Archmage of Menzoberranzan has lived a life of partying and magical study. But this is now to end House Baenre needs priestesses to restore their power so she is sent to Arach-Tinilith to train to be a priestess. After meeting with a human warrior Liriel is intrigued with the world above but has a problem going there, as she would lose all her drow magic. But when she finds out about rune magic and acquires a powerful amulet the Windwalker. She can carry her magic with her as she quests to carve the rune that will allow her to permanently wield her magic outside of the underdark. Along the way she joins up with the human warrior Fyodor the Rashemen beserker who also needs the Windwalker to control his magic. When they lose the Windwalker to the Dragon Hoard drow mercenaries they must hunt them down to recover it.

This is one of my Favourite series I much prefer Liriel to Drizzt as she is still the amoral drow comfortable with who she is and what she wants As opposed to his self righteousness and constant whining about acceptance. Liriel is fun and a little evil.