Depiction in the series

Twilight's original home in Canterlot

Twilight lived in Canterlot until Princess Celestia sent her and Spike to Ponyville to oversee the preparations for the Summer Sun Celebration and make some friends. Twilight befriends the rest of the main characters, and remains in Ponyville to continue to study the magic of friendship. In A Canterlot Wedding - Part 1, Twilight says that Princess Cadance was her foalsitter when she was a filly.
Twilight tells the Cutie Mark Crusaders how she got her cutie mark in The Cutie Mark Chronicles. She says that when she was a filly, she studied magic on her own and wanted to attend Princess Celestia's School for Gifted Unicorns. At the entrance exam, Twilight was told to use magic to hatch Spike's egg, but her magic got out of control when she was startled by Rainbow Dash's sonic rainboom. Princess Celestia took note of her magical abilities and made Twilight her personal protégé. In Magical Mystery Cure, Twilight Sparkle completes an unfinished magic spell with her deep understanding of friendship. Princess Celestia tells her that Twilight is ready for the next stage of her life. She is transformed into an Alicorn and crowned a princess.

Love of books

In Friendship is Magic, part 1, Twinkleshine says Twilight is more interested in books than friends. Even after Twilight becomes good friends with the rest of the main characters, she continues to read and consult books. For example, she confidently joins a marathon after reading several books about running in Fall Weather Friends.

Rationality

Twilight attempts to observe and measure Pinkie Sense omens.

Twilight tries to be rational in unfamiliar situations. During the investigation in MMMystery on the Friendship Express, Twilight tells Pinkie Pie to stop making wild accusations, and they work together to find clues and solve the mystery. However, Twilight can be illogical in stressful situations. In Swarm of the Century, she hysterically suggests building a replica of Ponyville in less than a minute before Princess Celestia can see the parasprite infestation.
Twilight tends to be skeptical of unproven claims, such as her friends' belief that Zecora is an evil enchantress in Bridle Gossip, and Pinkie's "Pinkie Sense" in Feeling Pinkie Keen.

Knack for organization

Twilight shows her knack for organization in Winter Wrap Up. When the Winter Wrap Up becomes inefficient and uncoordinated, she organizes the teams and ensures that winter is wrapped up on time. Mayor Mare gives Twilight the official title of "All-Team Organizer".

Magical talent

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Twilight Sparkle is exceptionally talented at magic. In a flashback in The Cutie Mark Chronicles, Princess Celestia tells Twilight that she has never seen a unicorn with so much raw ability.