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A wiki is a collection of collaboratively authored web documents. Basically, a wiki page is a web page everyone in your class can create together, right in the browser, without needing to know HTML. A wiki starts with one front page. Each author can add other pages to the wiki by simply creating a link to a page that doesn't exist yet.
Wikis get their name from the Hawaiian term "wiki wiki," which means "very fast." A wiki is indeed a fast method for creating content as a group. It's a hugely popular format on the Web for creating documents as a group. There is usually no central editor of a wiki, no single person who has final editorial control. Instead, the community edits and develops its own content. Consensus views emerge from the work of many people on a document.
Moodle's wiki is built atop an older wiki system called Erfurt wiki: http://erfurtwiki.sourceforge.net.
In Moodle, wikis can be a powerful tool for collaborative work. The entire class can edit a document together, creating a class product, or each student can have their own wiki and work on it with you and their classmates.
It may be useful to think of a wiki's front page as a structured table of contents. Essentially, a wiki is organized by its links.
Setting up and editing a Wiki
For documentation on setting up a Wiki and for adding and editing pages, see:
Setting up: Adding/editing_a_wiki
Adding pages: Section on Adding a wiki page
Editing pages: Section on Editing a wiki page
Printing pages: Wiki print