# Find the transfer function of a basic block diagram

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.

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.