I'm new to Control Systems. I've been given this block diagram and I would like to find the overall transfer function. How can I do it? I was thinking about simplifying the diagram by placing in parallel C(s) and R(s), but I don't think it is the right approach.
This is actually quite simple when one understood the concept, I'll try to make the start and you can solve the rest from there on your own.
You want to get a function that describes $y$ in terms of $v$, so you just work your way back from the end. Let's call the edge that goes into the $G(s)$ block $x$. Then we can write for the last part of the block diagram: $$ y = G(s) \cdot x$$ Now we can move on further through the diagram, by replacing $x$ with what it actually is, a sum of the edges that come out of $C(s)$ and $R(s)$. From here it's mostly rinse and repeat.
Eventually you will have a function that contains only your input and, in case of a feedback like here, also your output, which you can then solve for $y$. This yields the transfer function.