How do I approach professors for reading courses? 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.
I think the best approach would be to find out when the professor will be in his office and approach him and ask (or wait outside his class until class ends). I think he would appreciate having someone be interested in his work and maybe agree - after all, a university is meant for knowledge sharing right? 

You're right, if he is on sabbatical then there's nothing you can do. You will probably have to show that you are really interested and aren't there to waste his time.