Genes coding for strategies favouring assisting relatives can spread in populations if the benefit to the relatives multiplied by a coefficient of relatedness is greater than the cost to the actor. This idea is formalised in Hamilton's equation:
rB > C.
The theory of kin selection successfully models much of the apparently-altruistic behaviour in the world. It explains the love of mothers for their children. It shows that an individual-centric perspective on the natural world is incorrect - organisms are built to care about others besides themselves.
The theory of kin selection has roots dating back to Darwin, but it was first formalised by Hamilton in 1964. George Price contributed a slightly improved formalisation in the 1970s - which showed how kin selection could favour spite - as well as altruistic behavior.
Kin selection has been a tremendously productive theory. However in modern times much mud slinging against kin selection has taken place by advocates of a supposedly alternative theory of the evolution of social behaviour: group selection. Here we will attempt to set the record straight on the topic.