transfer function of electrical circuit (Beginner)
Two ways I can think to do this off the bat are this but they may not be the simplest:


Treat the first stage as a voltage divider so 
$$ V_{mid} = V_{in}* \frac{Ls||(R+1/Cs)}{R+Ls||(R+1/Cs)} $$
and then treat the second stage as another voltage divider so
$$ V_{out} = V_{mid}*\frac{1/Cs}{1/Cs+R} $$ and then put the two equations together to get your Vout/Vin which is your transfer function.
You could use the pi delta transform to convert both R's and L to 3 alternate elements and then one of them would be in parallel with C which can be simplified. The first vertical transposed element wouldn't matter anymore because it's an applied voltage so what you have left is a single voltage divider, which directly relates Vin and Vout.


Personally I'd go with option 1 because I've done almost all the work for you there.