I have just started my phd program this semester, I have not worked before on $C^*-$algebras, my master was on Geometry. In my university only reading courses are offered. I have to learn $C^*-$algebras. I have not taken any courses on functional analysis too. I am studying the book " $C^*-$algebras and their automorphism groups" by Pedersen, I usually google each topic and take a look at Book by Murphy too. But I could not find a good resource that give me a good prospective, for example how should I use Gelfand representation in problems. I mean I am learning topics, but I cannot learn with deep depth that I can use stuff like tools in my work. And Also I undestood that Functional analysis is a priority for $C^*-$algebras, but I cannot find a good book for understanding deeply materials like weak and weak$^*$ topology. When I read theorems I understand them, but I could not understand these topics as well as I give ideas for solving theorems on my own, and I cannot enjoy studying. I would appreciate if you recommend me some good books for self studying both Functional analysis and $C^*-$algebras.
My suggestion would be to consider Conway's "A Course in Functional Analysis". It even includes a basic chapter on C$^*$-algebras and von Neumann algebras.
Pedersen's book is wonderful in the sense of how concise he could write, but has a couple problems: one is that it is too deep, in a sense, so it is definitely hard for a beginner; and a second problem is that he (naturally) emphasized topics he did research, but that are not of much interest today.
You could also take a look at the first chapter in Davidson's C$^*$-algebras by Example.