The essay "Humour used as a double edged sword" not only explains these theories and how they work, but it also talks about why we use humour and its four functions.


1) Identification
2) Clarification
3) Enforcement
4) Differentiation


The first 2 are used to unite people while the 2nd two are used divide certain groups from others.


Identification
This is an ice breaker.  This is when you're getting to know someone and want them to like you so you tell a joke to make them laugh.  Now the conversation is initiated and ye're now friends!


Clarification
This is putting forth an opinion.  You win over the approval of the people you're talking to by making a joke that makes them laugh and simultaneously agree with you. 


Enforcement
This corrects unacceptable behavior.  This would be when your friend does something stupid which ends badly for them and those involved.  His or her friends will make fun of them and joke at their stupidity.  As a result of this kind of humour, the individual will refrain from doing the act againg in case they get mocked.


Differentiation
This humour contrasts oneself from others when standing on a particular issue.  For example, if a non religious person jokes that God is an invisible floating man in the sky, they immediately separate themselves from religious people while also making alliances with non religious people in a comical manner.


I've looked at many websites (which are listed in a previous post) and read a couple of books on the subject of humour and how it works.  They all talk about these theories and functions in different ways.  The two sources that were of most use to me were "Humour as a double edged sword " by John C. Meyer and "The joke and its relation to the Unconscious" by Sigmund Freud.  Freud talks about the Analytical, the Synthetical and the Theoretical aspects of humour, however its along similar lines of what I've already explained.