When I studied representation theory for the first time it was only focused on finite groups. It was the second half of a one semester course in group theory, and the book employed was "Representation Theory: A First Course" by Harris and Fulton.
Currently I'm studying Quantum Field Theory, and regarding spinors and quantum fields with spin, I'm interested in the representation theory of the Lorentz group.
I know the description of the fields with various spins is tightly connected to the irreducible representations of the Lorentz group.
Unfortunately, though, most traditional textbooks in QFT take a stand to not do a rigorous treatment of the matter, nor present a mathematicaly pleasant notation or definitions. Most of them speak quite loosely of the subject, that it doesn't even look connected to the representation theory I saw in the course I took.
Considering this, what I'm looking for is a book or lecture notes which presents a mathematicaly rigorous approach to the representation theory of the Lorentz group and also establish in a mathematicaly correct way the connection to quantum fields with spin and the representations of the Lorentz group. Is there such a resource out there?