what are the main sociological theories of education?

Answer 1

Functionalism- as societies get more complex, formal education systems are needed to produce the trained personnel required for modern careers.

Conflict theory- education serves to allocate (unequally) scarce good jobs, and also to indoctrinate the working class into middle class mores.

Answer 2

Functionalist, Marxist and Weberian

Here's the Functionalist view of Durkheim to start you off
Durkheim argued that education has many functions:

To reinforce social solidarity
History: Learning about individuals who have done good things for the many makes an individual feel insignificant.
Pledging allegiance: Makes individuals feel part of a group and therefore less likely to break rules.
To maintain social roles
School is a society in miniature. It has a similar hierarchy, rules, expectations to the "outside world". It trains young people to fulfill roles.
To maintain division of labour.
School sorts students into skill groups, encouraging students to take up employment in fields best suited to their abilities.

Also look at the labelling theory and look at the work of Merton