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The Creation of Cortana
HaloReach - Cortana
If any figure besides Master Chief stands at the center of the Halo universe, it's Cortana. The sentient AI that has consistently been by Master Chief's side was actually created using a flash cloned copy of Dr. Catherine Halsey's brain. Of the twenty clones created, one once survived. Halsey used this single clone to map her brain, her personality, and even her memories and values, into Cortana. Cortana began as a copy, but since her creation, she has become so much more.
Notable history

First Meetings
Cortana grew attached to Master Chief long before her literally attachment throughout the series. She was first integrated into Master Chief's MJOLNIR Mark V armor during a training exercise devised to test their compatability.The team passed, of course, with flying colors. Cortana was then installed into the UNSC Pillar of Autumn and did her best to return to the front lines of the war effort to aid the SPARTANs. Her expertise in bypassing or co-opting Covenant technology was unprecedented.
Notable quote:
“They let me pick. Did I ever tell you that? Choose whichever Spartan I wanted. You know me. I did my research. Watched as you became the soldier we needed you to be. Like the others, you were strong and swift and brave. A natural leader. But you had something they didn't. Something no one saw, but me. Can you guess...? Luck.”
— Cortana

The Fall of Reach
HaloReach - Finale
Cortana did eventually join Master Chief, but she was carried there with the help of Noble Team. Isolated in Sword Base with Dr. Halsey, Cortana was transferred into Noble Six's possession. With Reach nearly razed to the ground, Noble Team offered the ultimate sacrifice to reunite Cortana and Master Chief and save the Pillar of Autumn.The significance of Halo: Reach to the story of Halo should not be underestimated. Cortana's return ignited the fundamental beginnings of the game universe. It was Cortana who entered secret coordinates into the Pillar of Autumn that would discover the first Halo.
Notable history

A Working Relationship
Here I skip some of the events of the Halo universe to specifically stress the importance of Cortana and Master Chief's relationship. Cortana chose Master Chief as a host for their psychological compatability as much as their vocational compatability. Cortana is incredibly witty and jokes with Master Chief throughout their journey. The two have a genuinely strong relationship and both show an incredible loyalty to eachother, well beyond either her programming of his duty. Their connection remains one of the strongest friendships in video game history.
Notable Quote
“I am your shield... I am your sword.”

Capture and Rescue
Halo 4 master chief cortana
Their partnership was most tested during Cortana's capture aboard the Gravemind. While Master Chief fought on Earth, Cortana was undergoing extreme torture. It was her loyalty and trust in Master Chief that let her maintain her sanity and avoid destruction.Rescued at last, Cortana and Master Chief successfully activated and destroyed Installation 08. Trapped in wreckage, floating through space, and with Master Chief in deep cryogenic sleep, Cortana begins writing the history of the Forerunners and Humanity. For four years, seven months, and ten days, she waits - until the beginning of Halo 4.
Notable Quote
“I'll miss you.”
— Cortana to Master Chief, closing himself in a Cryotube