Ordinary algebra developed very gradually as a kind of shorthand, devised to abbreviate the discussion of arithmetical problems and the statement of arithmetical facts.
We were forced to abbreviate our trip due to the bad weather.
Abbriviate words like teaspoon and tablespoon to tsp and tbsp, respectively, to save space when writing recipes.
People often abbreviate names of universities to their acronyms, for ease of conversation.
Please abbreviate the months when writing dates in this document.
When transcribing, you should abbreviate words to speed up the process.
In order to avoid confusion, I never abbreviate my name in my signature.