Which theory argues that societies progressed through various stages from preindustrial to industrial to post-industrial societies?

Evolutionary theory of social change.

Already in the 19th century, early sociologists began to apply the Darwinian ideas of biological change over time to sociological changes over time.  

Pre-industrial society refers to the time before mechanization, when agriculture and handcrafting were the order of the day.

Industrial societies began to take shape with the tools and machines and sources of power introduced during the Industrial Revolution, beginning in the second half of the 18th century.

A "post-industrial" society still has industry active in it, but the focus of society and economy has shifted from manufacturing of goods to providing services and information.