You can rest assure that I’m sending this book at early of next week.
Can anyone tell me which preposition is the right choice?in or at? And also is it correct to say “at the start of next week” like you would say to last day of week as “at the end of the week”?
You can rest assured that I’m sending this book early next week.
That is sufficient.
“early next week”
“at the start of the week”
Either is OK.
Will the reader know I’m referring to next week in the sentence “at the start of the week” without the word “next”? In “early week” usage, can you explain to me why it can be used without preposition? Another thing is, as I’m writing a letter as much formal as i can, I would like to if it would still be correct to say “kindly rest assure that…” in the place of “you can rest assure that…”. Thanks for your help. I really appreciate it. 
Bulone, you are making problems for yourself. I provide two alternatives.
Rest assured that the book will be with you early next week.
I assure you that…
I’m just trying to understand how my sentence will be perceived by the other side in different constructions. It is palpable than anything else that I can just copy and paste your sentence and be done with my letter. Like you said earlier, there would be no problem. But, I’m not here to learn copy and paste nor do I want to be a sheep. I’m here to learn language properly and eventually expand my limit to non existence. Native people ,like yourself, is a tremendous asset to this process and I really do appreciate you sparing your time to help people out here. Not many people are generous enough to do that. Sorry to hear that you don’t see my posts in the way I intended. Thanks for you help so far.