What is an Abbreviation? 

An abbreviation is a shortened form of a word. Abbreviations are handy when compressing a long stretch of writing to make for easier reading. Instead of writing the name of an organization in full, you can simply use an abbreviation to reduce the word length of your writing. It is noteworthy, however, to remember that certain abbreviations should not be used in formal writing. Besides, a reader may not be familiar with an abbreviation, so caution should be maintained when abbreviations are used. A quick workaround here is to state the full meaning once before subsequently shortening the word or phrase.

Acronyms and Initialisms

There are different varieties of abbreviations. For example, initialisms and acronyms are abbreviations formed when the first letter of the constituting words in a phrase or name are combined. Initialisms and acronyms are usually written in capital letters to differentiate them from other words. 
Though formed from a series of first letters, acronyms are not pronounced as such but as a single word. So, you have the acronym UNESCO that stands for the United Nations Educational, Scientific and Cultural Organization. Another example is NATO which stands for the North Atlantic Treaty Organization. 

In contrast to acronyms, initialisms are not pronounced as a single word but as a series of letters. WHO, for example, stands for the World Health Organization. It is pronounced by mentioning each constituting letter and not the word "who" as would be expected of an acronym.
When using an indefinite article before an initialism or acronym, the rule is to choose an article that corresponds to the sound of the word and not necessarily the first letter. 

Abbreviations for Courtesy Titles and Academic Degrees

Abbreviations are also usually used when naming academic degrees such as Bachelor of Science, Doctor of philosophy as well as titles such as doctor, miss, mister, etc. While British English doesn't require you to add a period after title abbreviations, American English demands a period after title abbreviations. 

Common titles are:
Mrs. = Mistress, Mr. = Mister B.Sc. = Bachelor of Science, Ph.D. = Doctor of Philosophy Dr. = Doctor 
You can choose to use or discard the period when abbreviating academic degrees.  Choose a style and be consistent with it in your writing. However, when used as a title, academic degrees following a name are set off by commas: Paul Duke, Ph.D., is the head of lead researcher of the department.

Latin Abbreviations
Latin abbreviations include:
 et al. = et alibi which means "and others." 
a.m.. = ante meridiem which means "before midday."
etc. = et cetera which means "and so forth"
Note that a period is used with these abbreviations.

Other Common Abbreviations
There are many abbreviations you can use. However, styles differ, and so you have to be sure which one works well for your writing. For example, some may shorten Tuesday as Tue. while others may go with Tu. Some styles may not require periods, but others do. But if you are not sure, you can never go wrong including a period.
E.U. (European Union) U.K. (United Kingdom) are common abbreviations for places.
Units of Measurement
kg. (kilogram) km. (kilometer) and m. (meters) are common abbreviations for units of measurement. 

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