Quadratic forms play a huge role in math. This leads one to wonder: Is there a theory of cubic forms, quartic forms, quintic forms and so on? I have failed to discover any. Is there any such theory? If not, is it because: 
* It is not as interesting as quadratic forms? 
* It is so hard that no-one has yet written about such a theory? 
* It is already deeply infiltrated in math and only some smart people know about it?