Period or Full Stop
The primary use of a period is to end a sentence. Its second important use is for abbreviations. There are stylistic differences here. I will discuss both.
Martin Fowler, author of Modern English Usage, says that we should place a period at the end of an abbreviation only when the final letter of the abbreviation is not the final letter of the expanded word. For example:
Jesus Christ was born c. 4-6AD
The abbreviation is for the word “circa” – as it ends in an ‘a’ and the abbreviation is normally ‘c’ – we include the period.
Mr Jones was happy to see his wife
St Patrick lived in Ireland
In the first case above, “Mr” is an abbreviation for mister. Because mister ends in an ‘r’ and the abbreviation includes that ‘r’, we omit the period.
The other use of the period for abbreviations is to always include the period, regardless of whether the final letter is included.
Mr. Jones was happy to see his wife
If an abbreviated phrase is pronounced, we do not include periods. For example: NASA is correct, N.A.S.A is incorrect. In some cases the periods are omitted even when the word is not pronounced, usually because it is a very commonly known term. For example: UCLA (University of California, Los Angeles).
In the case of a word like et cetera (etc.,) we always include the period.