One of the biggest battles I face as a high school English teacher is the plague of “would of”, “could of” and “should of”. 

These incorrect terms have arisen from the corruptions of “would’ve”, “could’ve” and “should’ve”. Of course, those are contractions of “would have”, “could have” and “should have”.

The irony is that people use “would of” instead of “would’ve” because they think they are speaking or writing better English. 
However, using “of” instead of “have” is never correct. 

If you really want to set yourself apart from the masses, this is a great place to start. Say it correctly and write it correctly. Join the resistance, and lead by example.