Cornelius is a direct descendant of the Renaissance-era scholar and magus Cornelius Agrippa von Nettesheim. Contrary to his appearance - likened to "an agreeable youth in his twenties" in the novel - he is over 50 years old and has a cruel disposition.
He studied at the London branch of the Mage's Association along with Touko Aozaki and Souren Araya. The three of them had a pretty good relationship until their graduation. Alba wanted the title "Red" but it was given to Touko resulting his inferiority complex.
Before the events of Kara no Kyoukai, he was supposed to be the next director of a Sponheim Abbey that was affiliated with the Mage's Association.
He and Touko were on good terms when they were students until Touko surpassed him in their study of Runes. He is so obsessed with this inferiority complex that he occasionally becomes deranged when speaking of her.
Alba views reaching the Akasha is a useless effort but he teams up with Araya to kill Touko.
Kara no Kyoukai
Chapter 5: Paradox Spiral
He joined up with Araya and came to Japan, not because of the latter's attempt to reach Akasha, but solely to kill Touko to prove his superiority.
Cornelius was first seen by Enjou Tomoe when he notice Shiki Ryougi was being followed.
When Touko and Mikiya Kokutou was examining the Ogawa Apartment complex, Cornelius was spying on them at a far distance.
Touko meets Cornelius in her exhibition, she gave Mikiya a talisman to make him invisible. He explains to Touko his involvement with the Ogawa apartment complex. He mentions the kidnapping of Shiki which shocked Mikiya. Mikiya revealed his presense to Alba and he believed Mikiya to be Touko's apprentice.
When Touko approach Cornelius inside the Ogawa apartment, Touko suggested to bring out Araya as he wasn't capable of facing her. Cornelius frustrated with Touko looking down on him casted his thousand degree sea-of-flames spell, Touko redirects it and nonchalantly uses it to light her cigarette. Touko use her Projection machine and Cornelius was swallowed by the cat familiar until Araya saved him. He was knocked out during in the fight between Araya and Touko.
Cornelius approaches Araya complaining to him about not keeping his promise in which he was suppose to kill Touko. Cornelius angry at Araya desires to kill her personally and calls her Dirty Red. Araya called Cornelius foolish for saying something he shouldn't have but hands over Touko head.
As he was about to leave, he notices Mikiya in front of him. In front of Mikiya, he sadistically plays with Touko's head and crushes it. As Mikiya runs away from Cornelius, he humms out a classic music while following him. As he caught up with Mikiya, Mikiya attempts to stab Cornelius with the paper knife. Cornelius knocks Mikiya out and attempt to torture him by smashing his head to the wall to vent out his frustration with his history with Touko. Cornelius realises that the Touko standing behind him was the result of him killing her earlier, he panics and wonders which is the real Touko.
He was devoured by Touko's familiar in the 'sealed box' after calling her by her nickname, "Dirty Red". Only at the end did he realize that he "shouldn't have gotten involved with monsters" like Touko and Araya.
There is a person who appears similar to Alba in Fate/Zero, but while it is hinted at possibly being Alba, the production staff of Fate/Zero doesn't confirm it. He is one of the Enforcers who participates in the 'cleansing' of the vampirism started by Norikata Emiya at Arimago Island.
In terms of raw power, Cornelius is amongst the high end of all the magi to ever appear in TYPE-MOON works, but he doesn't get a chance to fully display his abilities during the story. Despite being an overall superior magus to both Araya and Touko, they can be called monsters that far surpass him in battle capability. He also has a bad compatibility against Kayneth Archibald El-Melloi. His Sea of Flames can create a thousand-degree conflagration in less than two seconds using high-speed incantations, so he can be compared to a character in a fighting game capable of spamming Super Moves at will. He has a black hound familiar and as well as ether clumps, Slimes. He is also a puppeteer and was responsible for the system at Ogawa Mansion, where only the brains of residents were kept alive and connected to puppet bodies. His Origin is Refutation.