Let me begin by/trouble

[Xinfu]

Could you correct my English?

Dear Prof Eistein:

Let me begin by thanking you for your help last year. This time I have to apologise for troubling you again, because I hope you can grant me approval to stay in college throughout (=live in that place) the entire summer period, which usually only medical students are allowed to do, because the construction work near my house is still in progress, so buildings in the vicinity are all invaded by mosquitos and insects. Apart from this, the original weal-causing bug problem in my house has not been solved yet, and those bugs come out again occasionally and cannot be exterminated. So I hope you can give me this permission. I look forward to your favourable reply. Thank you.

Yours sincerely,
Henry Fowler