Renomalizabilty and triple/quadruple vertices

I read that a Lagrangian is renormalizable if it contains only triple and quadruple vertices, or at most four powers of the fields.
Where can I read more about the precise mathematical conditions?

This depends on the dimensionality of the fields. A 4-fermion interaction (such as the one in the Fermi theory of weak interactions) is not renormalizable. This should be covered in any QFT textbook. Peskin & Schröder is pretty standard, but there are of course others too.