From “Remembrance of the Daleks”
The Doctor: A long time ago, on my home planet of Gallifrey, there lived a stellar engineer called Omega.
Ace: Stellar? As in stars? Do you mean he engineered stars?
The Doctor: Ace!
Ace: Sorry. Go on.
The Doctor: It was Omega who created the super-nova that was the initial power source for Gallifreyan time-travel experiments. He left behind him the basis on which Rassilon founded Time Lord society. And he left behind the Hand of Omega.
Ace: His hand? What good was that?
The Doctor: No, no, not his hand literally. No, it was called that because Time Lords have an infinite capacity for pretension.
Ace: I’d noticed that.
The Doctor: The Hand of Omega is a mythical name for Omega’s remote stellar manipulator. A device used to customize stars with. And didn’t we have trouble with the prototype...
The Doctor: They.
Ace: And the Daleks want it so they can recreate the time-travel experiments? But you said that both Dalek factions can already travel in time.
The Doctor: Oh, yes, Daleks have got time corridor technology, but it’s very crude and nasty. What they want is the power that Time Lords have. And they’ll get that from the Hand of Omega. Or so they think.
Ace: And you have to try and stop them.
The Doctor: No, Ace, I want them to have it!
The Doctor: My problem is trying to keep Group Captain Gilmore and his men from getting diced in the crossfire.
Ace: So all this --
The Doctor: Is a massive deception, yes.
Ace: Well devious! So the Daleks grab the Hand of Omega and go and no one gets hurt! Brilliant!
The Doctor: Just one thing.
The Doctor: I didn’t expect two Dalek factions. And now I have to make sure the wrong ones don’t get their grubby little protuberances on it!
* * *The Doctor: The Hand of Omega is inside this box. The most powerful and sophisticated remote stellar manipulator device ever constructed.
Ace: Are you sure you want the Daleks to have it?
The Doctor: Absolutely. You know what you’ve got to do, don’t you? Yes, of course you do.
Ace: Is it alive?
The Doctor: In a manner of speaking, yes.
The Doctor subsequently tricks Davros into causing the Hand of Omega to make Skaro’s sun go super-nova, thereby destroying the Daleks’ home planet.
The Doctor apparently took the Hand of Omega with him when he and Susan escaped Gallifrey in a stolen TARDIS. Upon arriving on Earth in A.D. 1963, he left the machine at a London undertaker’s shop, intending to have it buried in a nearby churchyard. However, he left unexpectedly when Mr. Chesterton and Ms. Wright discovered the TARDIS at Totter’s Lane and didn’t get back to have it buried until during his seventh incarnation. However, after only six months on Earth, the Hand was used to destroy Skaro and sent back to Gallifrey.
From “The Happiness Patrol”
On the Earth colony planet Terra Alpha, the Doctor tells Trevor Sigma that his nickname at college was “Theta Sigma.”
From “Silver Nemesis”
Ace: How can she get to 1988?
The Doctor: She used the silver arrow, of course. And she had some basic, rudimentary knowledge about time-travel. Black magic, mostly.
Ace: Black magic?
The Doctor: And what you might call a nose for secrets.
Ace: So, it wasn’t just silver, this stuff that fell from the sky?
The Doctor: Unfortunately, Lady Peinforte discovered it was something rather more unusual. A living metal, vallidium.
Ace: Living metal?
The Doctor: Yes, with just one purpose: destruction.
* * *
Richard: What will my lady do when you possess the Nemesis?
Lady Peinforte: Why, first have revenge on that predictable little man. He will soon arrive, Richard, oh, yes. I expect him. This time there’ll be a reckoning with the nameless Doctor whose power is so secret, for I have found his secret out.
* * *
The Doctor: Vallidium was created as the ultimate defense for Gallifrey, back in the early times.
Ace: Created by Omega?
The Doctor: Yes.
The Doctor: And Rassilon.
The Doctor: And none of it should have left Gallifrey. But, as always with these things, some of it did.
Ace: So you had to try to stop Lady Peinforte --
The Doctor: Or anyone else.
Ace: -- from ever putting the three bits together.
The Doctor: Yes, so I launched the largest piece into space...
Ace: But you got your sums wrong.
* * *
The Doctor: The rockets are now locked in to your destination. Now, let’s see how the Cyber Fleet is progressing. Right on course.
Nemesis: And I am to destroy the entire Cyber Fleet?
The Doctor: Forever.
Nemesis: And then?
The Doctor: Reform.
Nemesis: You will need me in the future, then.
The Doctor: I hope not.
Nemesis: That is what you said before.
The Doctor: Enough.
Nemesis: And after this, will I have my freedom?
The Doctor: Not yet.
The Doctor: I told you when. Things are still imperfect.
* * *
Ace: The Doctor’s not going to just give you the bow. Tell her, Doctor. Tell her.
Lady Peinforte: Doctor who? Have you never wondered where he came from? Who he is?
Ace: Nobody knows who the Doctor is.
Lady Peinforte: Except me.
Lady Peinforte: The statue told me.
Ace: All right, so what does it matter? He’s a Time Lord, I know that.
Lady Peinforte: (laughs and shakes her head) Well, Doctor?
The Doctor: If I give you the bow?
Lady Peinforte: Your power becomes mine, but your secrets remain your own.
The Doctor: It’s all over, Ace. My battle -- all my battles. I’ve lost. I can only surrender.
Lady Peinforte: Yes.
The Doctor: But not to you. The Cybermen will have the Nemesis.
Cyber Leader: This is most rational, Doctor.
Lady Peinforte: But I know your secrets!
The Doctor: Very well, tell them.
Lady Peinforte: I shall tell them of Gallifrey, tell them of the old time, the time of chaos.
The Doctor: Be my guest.
Lady Peinforte: Your secrets --
Cyber Leader: The secrets of the Time Lords mean nothing to us.
The Doctor: Exactly. Thank you for coming to the 20th century and giving me assistance. Thank you for bringing the arrow. You may go now.
Lady Peinforte: What?
The Doctor: You had the right game, but the wrong pawn. Check.
At some point, it would seem, an amount of vallidium, the mysterious living metal created by Omega and Rassilon, crashed to earth and eventually came into the possession of Lady Peinforte in seventeenth century England. She had it fashioned into a statue of herself, only to discover the metal’s sentient properties. Whatever plans she had for it were foiled by the Doctor, apparently earlier in his seventh incarnation since she recognized him visually. At some point, the statue revealed to her the dark secret of the Doctor’s true identity. The Doctor was able to launch the body of the statue into solar orbit encased in a meteorite. However, due to a miscalculation, the meteorite came near the earth every 25 years, its malevolent influence causing calamities. In the months to follow, Lady Peinforte hatched a plan to regain the statue and exact revenge on the Doctor when it eventually crashed back to earth in 1988. She seems to hint that the Doctor has something to do with the time in Gallifreyan history before the founding of Time Lord society and that the Doctor is not or not just a Time Lord. It is also possible that the sentient metal Nemesis is composed of is the same substance that gave the Hand of Omega its strange powers and apparent intelligence. It seems that vallidium may have been invented during the time before the establishment of Time Lord society to protect Gallifrey from some great enemy, perhaps by destroying that enemy entirely. Omega was then able to use this material to create the remote stellar manipulator that unlocked the secrets of time-travel and allowed Rassilon to make them Time Lords.
From “The Greatest Show in the Galaxy”
The Doctor: I have fought the Gods of Ragnarok all through time!
Ragnarok 1: You are in our true time-space now, Doctor. There is no appeal beyond its confines to any other!
The Doctor: Don’t tell me, let me guess. Now you want me to...
Ragnarok 1: Entertain us!
Ragnarok 2: Entertain us!
Ragnarok 1: Or die! So long as you entertain us, you may live!
Ragnarok 2: When you no longer entertain us, you die!
The Doctor: Predictable as ever, Gods of Ragnarok! As I think it’s been said before -- or was it after -- you ain’t seen nothin’ yet!
These “Gods of Ragnarok” are apparently a nihilistic triumvirate from another dimension who prey on imaginative beings to be used as entertainment. The Doctor seems to have a history with them, though it would seem he never before encountered them face to face.