Question

Which early school of psychology relied on a method called introspection?

Answer 1

The  early school of psychology that relied on a method called introspection was: Structuralism

Structuralism teach that in our personal life, we need to analyze various aspects such as behavior, human cognition, and culture in order to create a relationship with another human. 
And in order to fully found out those things, every one of us needs to ask and see it within ourselves (introspection) and reflect what we see with other human being