Karazhan is located in Deadwind Pass on the sub-continent of the Eastern Kingdoms on Azeroth. Existing long before Medivh inhabited it, it is unknown who originally built Karazhan or who now resides within its walls.
During the first war the tower was inhabited by Medivh, his butler Moroes, his cook Cook and his then-apprentice Khadgar. Garona also resided here as an emissary in the same time of Khadgar's apprenticeship. Sargeras allowed Medivh to freely explore Karazhan. It is said many strange and disturbing visions lurked within the tower, and Moroes was known for wearing blinders to avoid seeing them. Much of the story from this era is presented in the novel The Last Guardian.
Recently, despite Medivh's absence, a new power seems to have made its home in Karazhan. The Black Riders of Deadwind Pass, though rarely seen, have a connection to Karazhan. However, no one knows who their master is. One recent sighting is cause for concern — the Black Riders seek the Scythe of Elune, a powerful artifact with the ability to summon the vile Worgen into this world.
It is believed that all ley lines on Azeroth lead to a location under Karazhan.
Worldofwarcraft.com says the following about Karazhan:
The decrepit tower of Karazhan once housed one of the greatest powers Azeroth has ever known: the sorcerer Medivh. Since his death, a terrible curse has pervaded the tower and the surrounding lands. The spirits of nobles from nearby Darkshire reportedly walk its halls, suffering a fate worse than death for their curiosity. More dangerous spirits wait within Medivh's study, for it was there that he summoned demonic entities to do his bidding. However, the brave and foolish are still relentlessly drawn to Karazhan, tempted by rumors of unspeakable secrets and powerful treasures. Forge a group of ten stalwart heroes, and journey to the tower in Deadwind Pass — but be warned that only those who have achieved level 70 should dare enter.
For a more Detailed look into The Ivory Tower visit http://www.wowwiki.com/Karazhan.