Time

Time is a fundamental physical quality, measuring the duration of events and the intervals between them. It can be seen as part of the fundamental structure of the universe, a dimension in which events happen in sequence. Space-time vessels, such as TARDISes, could travel along this dimension in the same way that ordinary space vessels could travel along the other dimensions.

Explanations of time
Philosophers and scientists among humans and many other species struggled to define and explain time, but only the Time Lords achieved a full understanding.

The simplest definition of time is an operational one: pick a standard cyclical event, and define time as a count of the cycles. However, as an operational definition, this does nothing to explain what time actually is.

Isaac Newton was the first human scientist to attempt to fully explain time as a dimension, similar to the dimensions of space. Later scientists, culminating in Albert Einstein in the 20th century, were able to show how the dimensions of space and time could be unified into a single continuum, called spacetime.

Some human philosophers and scientists disagreed, but the Time Lords subscribed to this explanation as well - although, as Susan Foreman indicated, they knew that there were actually five dimensions of spacetime, not four. (DW: An Unearthly Child)

Structure of time
At a lower level, time was quantized, like a force, which the Master (in the guise of "Professor Thascalos") described as made up of particles known as chronons. (DW: The Time Monster)

Chronons, like other particles, could be detected and interacted with. (VG: City of the Daleks)

While the Weeping Angels were able to feed on the potential energy gained by displacing people into the past (DW: Blink), even they could not feed on raw time energy. Such energy, leaking out of cracks in the structure of the universe, absorbed an army of Angels at the crash of the Byzantium, completely removing them from history. (DW: Flesh and Stone) The Doctor suspected that the CyberKing walking over Victorian London (DW: The Next Doctor) and the Daleks invading Earth in 2009 had been similarly erased, and later saw Rory Williams absorbed by time energy. (DW: Flesh and Stone, Cold Blood)

Artron energy was also in some way connected with time, in a manner that was possibly too complicated for Time Lords to fully explain to humans. (DW: Four to Doomsday, The Deadly Assassin, Dalek, etc.)

Time travel
New connections between different points in spacetime could be created: for instance by time windows created by warp drives (DW: The Girl in the Fireplace); time storms created by Fenric (DW: Dragonfire, Silver Nemesis, The Curse of Fenric); or the cracks in the skin of the universe, which suddenly appeared at various times and places in the universe after a temporal explosion. (DW: Flesh and Stone, The Vampires of Venice)

Furthermore, travel from any point to another was possible by passing through the Time Vortex, by using a vehicle such as a TARDIS or Dalek time machine (DW: The Chase, etc.) or a device such as a vortex manipulator (DW: Utopia, The Sound of Drums, TW: Everything Changes, etc.), by creating a wormhole such as a time corridor (DW: The Evil of the Daleks, etc.), or even through direct psychic teleportation. (DW: Planet of the Spiders)

Other races eventually learned to travel through time. These included the Daleks (DW: The Chase) and humans. (DW: Invasion of the Dinosaurs) In the 51st century, humans established the Time Agency. (DW: The Talons of Weng-Chiang, The Empty Child)

The Time Lords, however, tried to keep strict controls on "unauthorised" use of time travel by other species. (DW: The Time Warrior, The Two Doctors)

Changing history
The Tenth Doctor laboured in an effort to explain to humans how time is misunderstood and never strictly linear, that it is made up of "wibbly-wobbly, timey-wimey... stuff." (DW: Blink) Another time, he tried making it easier for his companion, Martha Jones, to understand by referencing Back to the Future to explain the mechanics of the "infinite temporal flux"; if the Carrionites succeeded in freeing the rest of their kind and toke over Earth, Martha would vanish as the future she came from would no longer exist. (DW: The Shakespeare Code)

Travelling into the past allowed changing the future. As the Eleventh Doctor put it, "Time can shift. Time can change. Time can be rewritten." (DW: Flesh and Stone)

However, erasing events from history did not always automatically change the future. Time travellers were able to remember the "original" timeline (DW: Flesh and Stone), unless the erasure directly affected their life (DW: Cold Blood), in which case they had to make an extraordinary effort to do so. Blocking chronons (e.g., with a TARDIS or a special-built device) could prevent objects from vanishing even though they no longer had a past. (VG: City of the Daleks) In a similar way, a paradox machine could be built (e.g., from a cannibalised TARDIS) to allow time paradoxes to persist without effect. (DW: The Sound of Drums, Last of the Time Lords)

In a universe with time travel and a malleable spacetime, there would be no fundamental stable meta-structure to history. However, the Time Lords imposed one, which they called the Web of Time, which connected the fragmentary nodes of history into a single whole. (BFA: Neverland) This Web required maintenance, as when the Sixth Doctor explained that the destruction of Earth in 1985 would disrupt the Web. (DW: Attack of the Cybermen)

Even in the post-Gallifrey universe, some events were fixed points which must happen. One example was the volcanic eruption of Mount Vesuvius at Pompeii. (BFA: The Fires of Vulcan, DW: The Fires of Pompeii) Changing fixed point events required highly advanced technology, and doing so could cause major damage to the continuum. (VG: City of the Daleks)

Other moments were in flux, allowing minor changes to history. Some events even allowed dramatic changes in history, especially after the demise of the Time Lords in the Last Great Time War. (DW: The Unquiet Dead) An example of this occurred in 2020, when a drilling operation in Cardiff altered the future of the Earth by bringing humanity into contact with the Silurians, which could have led to either a peaceful relationship or a devastating war. The Doctor described these events as opportunities. (DW: The Hungry Earth, Cold Blood)

Parallel universes and alternate timelines
At historical choice points, the timeline naturally diverged, creating two parallel universes. (DW: Inferno, etc.) These parallel universes could be reached through the Time Vortex before the Last Great Time War, but in the post-Gallifrey universe this became much more difficult, and dangerous to the structure of spacetime. (DW: Rise of the Cybermen, Doomsday)

Changing history by time travel, in a way inconsistent with the meta-structure of spacetime, would create an alternate timeline, which had a similar effect. Historically, the Time Lords would alter history to prevent these alterations from having ever happened, negating the alternate timeline in all but the memories of time travellers who participated in them. (DW: Day of the Daleks, NA: Timewyrm: Exodus, DW: The Big Bang, Good Night.) However, some time travellers were left confused as to how they can accept multiple different realities in their heads. Even Time Lords such as the Doctor don't how to explain this properly. (DW: Space, Bad Night/Good Night) In the post-Gallifrey universe, the Doctor and others often acted on their own to do the same. (DW: Turn Left, Last of the Time Lords, SJA: The Mad Woman in the Attic, etc.)

Personification
Like other cosmic principles, time is embodied by an Eternal, named Time, who chose the Seventh Doctor as her champion. (NA: Happy Endings)