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Abbreviations and acronyms are shortened forms of words or phrases. Generally, abbreviations are not acceptable in academic writing (with some exceptions, see below) and acronyms are (providing they are used as shown below).
As academic writing is formal in style, most abbreviations should be avoided. Even the common ones shown below:
Some common ones to avoid
Avoid e.g. and i.e., instead use for example and for instance.
Avoid etc. There isn't really an alternative, so rewrite the sentence.
Avoid dept, govt. Use department, government.
Avoid NB, instead use note that.
Avoid vs or v, instead use versus or against (except in Law reports or cases)
Some acceptable abbreviations
Titles such as Mr. Dr. Prof. are acceptable when using them in conjunction with the individual's name i.e. Dr. Smith.
Some Latin phrases
et al. (short form of et alia - and others is acceptable when giving in text citations with multiple authors. The full stop should always be included afterwards to acknowledge the abbreviation. It does not need to be italicised as it is in common usage.
ibid. (short form of ibidim - in the same place) is acceptable if using footnote references to indicate that a reference is the same as the previous one. Again, always include the full stop to acknowledge the abbreviation. It is the convention to italicise this as it is less commonly used.
sic (short form of sic erat scriptum - thus it was written). This is used to indicate there was an error in something you are quoting (either an interviewee or an author) and it is not a misquote. It is added in square brackets but is neither italicised nor followed by a full stop i.e.
"it'd be great if unis [sic] could develop a person's self-knowledge"
Acronyms are acceptable, but use the name in full on its first use in a particular document (e.g. an assignment), no matter how well known the acronym is.
For example, on its first use in an essay you might refer to "the World Health Organisation (WHO)" - it would be fine to simply refer to "the WHO" for the remainder of the essay.