I am studying mathematics in a UK institution and it is not as common (or not common at all) for undergrads to do reading courses with professors as it is in the US. I would like to ask what would be a "good" way (sorry for the lack of adjectives to describe this) to approach professors regarding this matter? I have in mind what the topic will be and the main book I would be reading which matches one professor's field of interest.
How can I make an introduction that is not considered as "awkward" and when would be a good time for me to approach him if I plan to do my reading course starting from, say the coming October.
Besides, how would I know whether he would be willing to guide me as most professors seem to be very busy and one hour per week/two weeks is non trivial for them.
Moreover, what if he's going to be in sabbatical (although I won't know until I ask)?
Thanks in advance.
PS: A reading course is basically independent study, asking a professor to guide you through a topic/book etc, which is not graded nor having any credit.