Noun

1. The act of inquiring; a seeking of information by asking questions; interrogation; a question or questioning.
2. Search for truth, information, or knowledge; examination of facts or principles; research; investigation; as, physical inquiries.

Usage notes

According to Fowler's Modern English Usage (1926), inquiry should be used in relation to a formal inquest, and enquiry to the act of questioning. Many (though not all) British writers maintain this distinction; the Oxford English Dictionary, on the other hand, lists inquiry and enquiry as equal alternatives, in that order. Some British dictionaries, such as Chambers 21st Century Dictionary http://www.chambersharrap.co.uk/chambers/features/chref/chref.py/main?title=21st&query=inquiry, present the two spellings as interchangeable variants in the general sense, but prefer inquiry for the "formal inquest" sense. In Australian English, inquiry represents a formal inquest (such as a government investigation) while enquiry is used in the act of questioning; (eg: the customer enquired about the status of his loan application); both spellings are current in Canadian English, where enquiry is often associated with scholarly or intellectual research. (See Pam Peters, The Cambridge Guide to English Usage, p. 282.)

American English usually uses inquiry.