The Doctor's guitar

The Twelfth Doctor possessed an electric guitar and showed himself to be an excellent guitar player.

History
He used his own guitar when challenged to an "axe fight" by Bors, although the medieval audience did not understand the play on words. He played "Pretty Woman" when he noticed that Clara Oswald and were watching. (TV: The Magician's Apprentice)

He also played the same electric guitar in his TARDIS, this time playing Beethoven's Fifth Symphony while contemplating the bootstrap paradox. (TV: Before the Flood) He was playing "Amazing Grace" on the same guitar when Osgood contacted him about the Zygon uprising. (TV: The Zygon Invasion)

After being separated from his TARDIS and spending some time in Nevada, the Twelfth Doctor acquired a new electric guitar. He wrote a song inspired by his companion, Clara, using this guitar. (TV: Hell Bent) The Doctor later played Beethoven's Fifth Symphony in his office at St Luke's University, before first meeting Bill Potts in person. He later played the same guitar at a bar Bill went to, playing the song he wrote about Clara. (TV: The Pilot) Even when blinded by exposure to the vacuum of space, (TV: Oxygen) the Doctor could still play his electric guitar. (TV: The Pyramid at the End of the World)

When the First Doctor witnessed the Twelfth Doctor's TARDIS console room, he observed that the guitar was the only thing in the room that had been cleaned; the Twelfth Doctor tried to hide the fact that the guitar was his. (TV: Twice Upon a Time)

Behind the scenes
The model of the Twelfth Doctor's guitar is a Yamaha SGV-800 "Black Sparkle". The model he plays in Hell Bent is a Limited Edition "1966" Epiphone SG-400 Pro, in Cherry Red, with the addition of a Bigsby B5 Telecaster Vibrato. This model is a copy of the Gibson SG, the guitar that is most commonly associated with Tony Iommi, guitarist with Black Sabbath, as well as Angus Young, lead guitarist with AC/DC.

The AMP used in Before the Flood, is a modified version of the “Fender Mustang Ii Amplifier”, referencing Magpie Electrical from The Idiot's Lantern.