Use brackets to set off an explanatory reference, your own comments, or corrections within material you are quoting.
According to Smith, "Proton energy levels [in the accelerator] are consistently higher than expected."
[These comments were made before Brodier became aware of
Unless the documentation style you are following specifies otherwise, use the Latin term sic in brackets to indicate that material in a quotation is incorrect.
Freedman stated, "Various Indo-European languages such as Rumanian, Hindi, Hungarian [sic], and Serbian exhibit similar morphological patterns."[Hungarian is not an Indo-European language.]
Use brackets to enclose parenthetical material that is within material already in parentheses.
The first extant cosmological theories were developed by the early Babylonians and Greeks. (See Alan Lightman, Ancient Light [Cambridge: Harvard University Press], pp. 5-9.)
Use brackets to indicate the isotope of a specific chemical.