Adric

Adric was a companion to the Doctor in his fourth and fifth incarnations.

Early life on Alzarius
Adric was born and lived on the planet Alzarius. He was ranked as an elite and awarded a gold star as a badge for mathematical excellence because he could do large sums in his head. His brother Varsh was a member of a gang of teenage thieves; Adric wanted to join them but was denied. Varsh asked him the embarkation question "Where will you be when the starliner leaves Alzarius?" to which he replied he would be somewhere else entirely. This would be true; he would be onboard the TARDIS when it took off. To prove himself to the gang he attempted to steal river fruit but failed. (DW: Full Circle).

E-Space adventures
Adric hid aboard the TARDIS, as the Fourth Doctor and Romana would discover later. Cunningly, he pretended to share the agenda of the Three Who Rule, a trio of vampires who lorded over a small community. He then attempted to save Romana from being sacrificed but failed; both were saved by the Doctor. (DW: State of Decay)

After Romana
After Romana left, (DW: Warriors' Gate) Adric and the Fourth Doctor had many adventures together. They formed a bond of trust. The Doctor genuinely came to like Adric. (PDA: Divided Loyalties) Soon after returning to N-Space, the Doctor and Adric went to Traken and met Nyssa for the first time. After apparently dispatching the threat of the Master, and returning the Keepership to is rightful heirs, (DW: The Keeper of Traken) the duo travelled broadly. During this period, the Doctor constructed another version of K9, who then naturally joined them on their journeys. (DWA: Inter-Galactic Cat, Conundrum, Planet of Paradise, Plague World, Just a Small Problem)

At some point prior to the Fourth Doctor's attempt to fix the TARDIS' chameleon circuit, (DW: Logopolis), the Doctor dispensed with this newer K9.

With the Fifth Doctor
Adric's relationship with the Doctor deteriorated after the Fourth Doctor passed and Tegan and Nyssa began travelling in the TARDIS. (DW: Logopolis, Castrovalva) Adric actively believed that the girls were a hindrance to his relationship with the Doctor. But he also had a clear preference for the Fourth Doctor, whom he regarded as the "real Doctor", and whom he actively missed after spending time with the Fifth Doctor. (PDA: Divided Loyalties)

Often frustrated by his clumsiness, and fiercely competitive, Adric struggled to find a useful role among the others.

He eventually told the Doctor that he wanted to attempt a return to E-Space. After showing the Doctor his mathematical computations to engineer the return, Adric confessed that he truly wished to remain on the TARDIS. Tragically, he became caught up in an attempted Cyberman invasion at that time, which ultimately led him to give up his life by remaining on board a crashing spaceship. The ship, Captain Briggs' freighter, was traveling through time. With Adric onboard, it crashed into prehistoric Earth, causing the extinction of the dinosaurs. (DW: Earthshock)

Adric's death continued to haunt the Doctor for many years, as seen when his tenth incarnation watched Adric die again -- this time a manifestation of the TARDIS Matrix. (IDW: The Forgotten)

In an alternate version of these events, following interference by the Doctor during an attempt to recover his TARDIS, his sub-consciousness assisted Adric in breaking the final logic code on the Cybermen's computer, allowing Adric to crash land (though survivable) on Earth. Adric survived for 500 years, creating a City of Excellence and ruling over a sentient race of Scorpions that evolved rather than the dinosaurs. The world they and Adric inhabited was created by Adric from Block Transfer Computations. 500 years later, Adric met up with the the Doctor and Nyssa, and accompanied them back to the Victorian era. Adric finally died after helping the Doctor recover his TARDIS from Thomas Brewster. (BFA: The Boy That Time Forgot)

Personality
Adric was a genius mathematician. He was proud of his Elite status, claiming he was better than others as a result of it. Adric wanted to join his brother Varsh's gang, the Outlers, and attempted to steal fruit to prove himself. He stated he was tired of how he was pushed around on the Starliner. When his brother died he kept his belt which was the symbol of Outler membership. (DW: Full Circle) He pretended to go along with the plans of the vampires in a ploy to rescue Romana. (DW: State of Decay) Aukon sensed that Adric had the strength of spirit to survive the process of becoming a vampire. (EDA: The Eight Doctors) He ultimately gave up his life by remaining on board Captain Briggs's freighter in an effort to prevent it from crashing into the earth. He died holding his brother's belt. (DW: Earthshock)

Other information

 * The last word of the Fifth Doctor was "Adric?" (DW: The Caves of Androzani)