Lecture note recommendations for the endogenous growth model (EGM)
I think that the notes closely resembling what you are looking for - a gradual explanation of how the growth theories develop - are those from Acemoglu. Check his web page for slides and look in your school library for Intro to Modern Economic Growth. The slides are very detailed I think. 

Growth models are, I believe, presented very rigorously. Additionally, in my opinion, it is discussed how they are connected.