I have been studying for a while abstract algebra, group theory and complex variables (at the basic level of the books of Fraleigh, Humphreys and Gamelin.
I have also surfed through some books in number theory and know the basics, but somehow I feel that Multiplicative Number Theory is a little far from the usual approach that the basic number theory books tackle.
What would be your advise to tackle this Davenport's monograph for selft-study? Particularly I am interested in understanding the proof Dirichlet Theorem on Arithmetic progressions.
I think you have what it takes indeed already.
I would recommend the book "Introduction to Analytic Number Theory" by Apostol, https://www.amazon.co.uk/Introduction-Analytic-Number-Undergraduate-Mathematics/dp/0387901639/ref=sr_1_1?ie=UTF8&qid=1523644851&sr=8-1&keywords=Analytic+Number+tHeory+apostol.
In particular Chapter 7 is what you are after and it gets there bit by bit, just for some extra help.