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In British English, these abbreviations have been in use so very long that for the most part, they are considered first-class words in their own right and thus no longer retain the full stop at all times.

It is however, not uncommon to see the full stop retained when used in an address, or a salutation. Mid-sentence is generally omitted, as the sight of a full stop cropping up in the middle of a sentence tends to cause more consternation than the omittance of a punctuation technicality.

I read somewhere once that if the abbreviation ends with the same letter as the full word -e.g. Mister, Mistress, Doctor- then no closing full stop is necessary.

That said, N.Americans will always place one at the end of those honorifics.

[Because id est and exempli gratia are two separate words, they're properly abbreviated as i.e. and e.g..]

The two most widely followed style guides in mainstream U.S. publishing are The Chicago Manual of Style and The Associated Press Stylebook. They agree in endorsing the use of a period after Mr or Mrs. From AP Stylebook (2002):

Mr., Mrs. The plural of Mr. is Messrs.; the plural of Mrs. is Mmes. These abbreviated spellings apply in all uses, including direct quotations.

And from Chicago (fifteenth edition, 2003):

15.16 Social titles. Always abbreviated, whether preceding the full name or the surname only, are such social titles as the following:

Ms. Mrs. Messrs. Mr. Dr.

Publishers that follow either of these guides require a period after such social-title abbreviations, unless their house style guide overrules the standard guide on this point.

As a counterpoint, MLA Style Manual and Guide to Scholarly Publishing, second edition (1998) opposes using formal titles at all:

3.6.2 Titles of Persons In general, do not use formal titles (Mr., Mrs., Miss, Ms., Dr., Professor, Reverend) in first or subsequent references to men or women, living or dead (Churchill, not Mr. Churchill; Mead, not Professor Mead; Hess, not Dame Hess; Montagu, not Lady Montagu). [Exceptions for certain "women in history," such as Mrs. Humphrey Ward and Mme de Staël, and for certain titled nobles, such as Henry Howard, earl of Surrey, omitted.]

The tendency in British style appears to be against end punctuation of social titles. The Oxford Style Manual (2003) doesn't discuss the matter directly, but it consistently gives examples of Mr, Mrs, Dr, and the like without periods. For example:

Titles used as identification or clarification after a name normally are not capitalized, especially in US usage):

[Relevant examples:] Mr Gladstone, the prime minister; Dr Primrose, the parish vicar

And in the "Oxford Dictionary for Writers and Editors" section of The Oxford Style Manual, the entries are similarly consistent:

Dr doctor (before name)

Mr Mister. pl. Messrs

Mrs Missis, Missus (corruptions of Mistress)

Ms the title of a woman whether or not married (no point)

Oxford doesn't apply its "no point" rule across the board, however. The style manual takes the opposite approach in its treatment of military abbreviations—Cpl., Sgt., Lt., Capt., Maj., and Gen., for example—and of Jr. after proper names.

I was taught in school (British, Primary) that a Full Stop or Period was used at the end of Abbreviations i.e. it stood for the rest of the letters. So - Rev. for Rev*erend*, Capt. for Capt*ain*, Col., Prof. etc

But Mr, Dr, and the anomalous Mrs are contractions. A Full Stop after them conveys no added meaning. Logically, I suppose, Mr should be writtern M.r and Dr D.r, but that would be too confusing and, in any case, the meaning is clear without any Full Stop following.

That is not true of at least some abbreviations e.g. 'Rev the engine, Rev.' [your getaway driver is a clergyman!]; 'Col' means the lowest point between two mountain peaks; 'capt' is a poetic variant of 'capped' and appears on Shakespeare's memorial in Westminster Abbey; 'The Cloud capt Tow'rs,[http://www.westminster-abbey.org/our-history/people/william-shakespeare ]

Americans tend to place a period after Mr, Mrs, etc. The British and related speakers often don't.

I think it depends on the style guide. American Medical Association style is to omit periods in all abbreviations except middle initials, so: eg, ie, vs, Dr, Mr, etc. This is probably just the magazine's house style.

I follow the following convention:

Male: Mr.

Female: Mrs., Miss, and Ms

"No need to put a period after Ms (as in, Ms Prescott) since it's not an abbreviation."
-Lionel Trilling Professor in the Humanities, Guggenheim Fellow, and founder of the Logic and Rhetoric writing course at Columbia University, Professor Edward Tayler (Self-Help, page 8).

I take his advice on style above anybody in Chicago. I am indifferent about the American way of doing things otherwise. I should like to actually use the period after Miss, for indicating the presence of more letters, as described by Fowler, but it seems unpatriotic.

These are still abbreviations so technically should retain their full stops.

If you use full stops after abbreviations such as ie. and eg. then writing Mr. instead of Mr would increase your consistency.