@takashichea: Said serial killer, Uryuu, was descended from a family line of magi yet knowledge of this was lost among the more recent generations of his family. The magical book that Uryuu thought could summon demons was actually a book of spells that his ancestors wrote from centuries earlier and he didn't understand that the ritual circle he set up was actually for summoning a Servant. The Holy Grail recognized his "worthiness" of being a Master, but Uryuu lacked a medium to summon a specific Servant thus the Grail summoned a Servant with personality traits most similar to Uryuu, resulting in Bluebeard's summon. Uryuu has the magical ability and an adequate supply of mana, but he lacks the knowledge to properly use magecraft.
As for UBW, the storyline is supposed to be Rin's "route" from the visual novel.