The Doctor's mind

The Doctor's mind was the inner consciousness within the Doctor's brain.

History
During the Time Paradox Incident, the Daleks used a Mind Analysis Machine to forcibly ascertain the identity of the Third Doctor, projecting the familiar images of the First and Second Doctors on their screen. (PROSE: Doctor Who and the Day of the Daleks, TV: Day of the Daleks)

The Third Doctor once saw images of the Master inside his mind during a nightmare. (TV: The Time Monster)

When the Eighth Doctor was possessed by Zagreus and stabbed by Charley Pollard, he met the mental manifestations of his fifth, sixth and seventh incarnations in his mind when he nearly allowed himself to die, subsequently rallying himself with their aid to restore himself and retake control of the anti-time energies. (AUDIO: Zagreus)

Mr Clever attempted to take over the Eleventh Doctor's mind when trying to convert him into a Cyberman. The mind was subsequently split into two halves; 49.881% in the Doctor's control and 49.881% under Mr Clever's influence. The two sides differentiated, with Mr Clever's half coloured silver and blue with circuitry scattered around, while the Doctor's was orange with Gallifreyan symbols covering it. (TV: Nightmare in Silver)

Within the mind, the Doctor could apply a mental block to prevent intruders from seeing things he did not want them to see. (TV: New Earth, Nightmare in Silver) However, if the Doctor was purposefully connecting with another, namely Jeanne-Antoinette Poisson with the Tenth Doctor, they could see into his memories, so long as the Doctor maintained the connection. (TV: The Girl in the Fireplace) Once, the Eleventh Doctor rapidly connected his mind with Craig Owens' to speedily share information, although the process resulted in a mild headache. (TV: The Lodger)

Regeneration energy could also transfer the knowledge within the Doctor's mind to another. Donna Noble gained the Tenth Doctor's mind by touching his severed hand while it was infused with regeneration energy from a recent regeneration. However, given she was human, the Tenth Doctor had to remove all memory of himself from her soon after to ensure her mind did not burn from trying to possess a Time Lord consciousness. (TV: Journey's End)

The Twelfth Doctor could willingly enter his mind to quickly deduce problems when under extreme duress. While there, his mind took the image of his TARDIS while he worked out solutions. Given how quickly his mind processed information, what seemed like minutes to him was mere seconds outside his mind. (TV: Heaven Sent)

Behind the scenes

 * The use of the Mind Analysis Machine in Day of the Daleks was parodied in an installment of Doctor Whoah!, where the Doctor is flustered as his mind wonders toward a romanticised image of the Brigadier in his underpants, and he tries to convince the Daleks that it is nothing more than "a brilliant fiction" he concocted to distract them.