Posts like this one have always baffled me. I have taken a few complex variables courses in my time and it seems that every time I take a course like this, either the textbook isn't great at explaining how, for example, a circle "becomes" a straight line or the instructor isn't great at explaining the concept.
I'm currently looking at Ahlfors's Complex Analysis where Ahlfors introduces such concepts via Mobius transformations, but he does not go into great detail explaining the transforming of regions of the plane into various shapes and objects.
What are good resources for teaching oneself the visualization behind Mobius transformations (e.g. mapping a circle into a straight line and so on)?