MLA style guidelines are possibly the most flexible for the use of abbreviations in that they are more acceptable to use in MLA style than either Chicago or APA. When abbreviating common phrases or using country or state abbreviations, MLA guidelines don't require the use of periods. For example, you would write USA instead of U.S.A, HTML instead of H.T.M.L.
If you are abbreviating a person's name, use a period after each initial and insert a space before the next, for example: J. R. R. Tolkien, E. B. White, unless the individual abbreviates or writes their name a certain way for artistic reasons, such as ee cummings.
In MLA format, you can also abbreviate some common words such as "association" (assn.) "anonymous" (anon.) or "et cetera" (etc.), in which case you would use lowercase letters followed by a period. Common phrases like "miles per hour" or "beats per minute" can be abbreviated to "mph" and "bpm" without a period.
When abbreviating Latin phrases to denote examples or time, use lowercase letters separated by periods but no spaces, for example: "A.D.," "a.m." "i.e.," "e.g."
APA style is far more strict with allowed abbreviations. Guidelines set for APA style prescribe that abbreviations should only be used to allow for clear communication.
Generally, APA's allowable abbreviations are similar to those of MLA: don't use periods or spaces between letters unless in proper names. For example, "USA," "AIDS," "HTML," compared to "J. R. R. Tolkien." One notable difference is that in APA, if you are using a capitalized abbreviation as a descriptor, you would insert periods between letters, but not spaces: e.g. "U.S. President Barack Obama."
Latin abbreviations are handled the same way as MLA format: "etc.," "a.m.," "b.c." or to denote a reference, such as "2nd ed." or "p. 142."
Periods are not used in APA style for units of measurement, which should only be abbreviated when used with a numerical value, like "10 min," "75 mi" or " 350 lbs," except in the case of inch ("in.") to avoid confusion with the word "in." If a unit of measurement is used in a phrase without a number value, spell out the full word.
Chicago style is the most restrictive in terms of allowable abbreviations. It allows abbreviations to be used for common institutions (UCLA, FBI, UMass, UN) or corporations (CNN, IBM), famous people (MLK, FDR, JFK) or very common objects (TV, VCR, DVD) without the use of periods. When abbreviating country names in Chicago style (U.S.A., U.K., D.P.K.R.) you should use periods, but no spaces.
Mathematical units are abbreviated the same way as APA style, but should only be used in technical writing. The same goes for most location abbreviations, such as for states or territories. In formal prose, all state names should be written out in full. Chicago style only allows for state names to be abbreviated in full addresses, using the U.S. Postal Service's accepted abbreviations.
Other acceptable abbreviations (Latin phrases; references to time) are handled in the same way as APA style. For BC ("Before Christ"), AD ("Anno Domini") or the more-modern BCE ("Before Common Era") and CE ("Common Era"), newer Chicago style guides call for AD and CE to be used before the year they reference (AD 1254; CE 75) while BC and BCE should be used after (200 BC; 300 BCE).
Recent style guides are also making it common to suggest small caps for all capitalized abbreviations in Chicago style.