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Speedrunning is when an individual attempts to beat part or all of a video game as quickly as possible. This can include individual levels, specific objectives, or unique limitations as decided by the community or player.
Any% requires the runner to beat the game as fast as possible.
100% requires the runner to beat the game while collecting all key items or upgrades and doing everything important. 
Low% requires the runner to beat the game while skipping every key item or upgrade possible. If skipping everything is the fastest way to beat the game, there will not be a low% category separate from Any%. 
Individual Level (IL) runs refers to speedrunning a specific level/chapter in the game as fast as possible, rather than the whole game start to finish.
Main article: Tool-assisted Speedrun
Tool-Assisted Speedrunning is a kind of speedrun that uses tools to optimize every last frame. They therefore invariably contain feats that are humanly impossible.
Constructing a TAS is more like animating a movie than playing a video game, and requires much, much more patience than actual skill. Both TASes and Real-Time speedruns require concentration, dedication, planning, and far too much free time, but TASes are not listed on this wiki, and you can think of this as the video gaming equivalent of banning steroids. This wiki is about real time runs.
The most common way of TASing is using slowdown and savestates. Slowdown is when the game's framerate is slowed down to make it run slower, and savestates are used to save the progress during a project and you can revert to that point if a mistake is made later.
Multiple Game Speedruns
Multiple Game speedruns, also known as series run, means speedrunning all or some of the games in a series back to back.