Creoles are languages formed when speakers of many languages come into contact with each other.
Creoles at first develop as pidgins, languages which combine words from the languages of different speakers, though they tend to come mostly from the local prestige language. At first they are spoken without regards to grammar, however when children learn the pidgins, they turn them into creoles, complete with grammatical rules.
Creoles around the world
Creoles are generally not prestige languages, however in some countries, notably Haiti, Papua New Guinea, and Vanatu, creoles are official languages: Haitian Creole, Tok Pisin, and Bislama respectively, though co-official in these countries with French and/or English.
Creoles around the world tend to have very similar rules, though there are two schools of thought on this. One claims that the creole is based on a local substratum, with words from the prestige language. The other claims that the rules of creoles are part of a "language instinct," and fairly universal, under similar conditions. As the rules of creoles never correspond to the substratums of any of any of the languages that went into the mix, supporters of the substratum hypothesis generally argue that creoles either combine grammar from many languages, or all stem from a common creole anscestor. Regardless of their origin however, creoles tend to have fairly similar rules
Typology and Syntax
As they age, creoles tend to become more grammatically complex, a process usually called decreolization. Usually the grammar appears to approach that of the local prestige language, however sometimes there is no clear grammatical base for these developments, as in the Suriname creole Saramaccan.
There are however some critics of the notion of decreolization, such as Derek Bickerton, a prominent creolist, who argues that the apparent process of decreolization is actually a case of language shift along a sociolect.
Creoles are different from mixed languages, which undergo a process of lexical replacement. Mixed languages are relatively rare, and tend to have more complex rules than creoles, as they maintain the grammar of the substratum.