First, I want to thank all of you who have recommended
A fire upon the deep. Though I like to read science-fiction a lot, I had never heard about this book before hearing it praised here. I'm currently reading it now, and, wow, what a book! It had been a long time since I'd been enthralled by a book to this extent.
My question is, is
A deepness in the sky a direct sequel of the first book (i.e., taking place just after the end of the first book or shortly after, involving the same characters, etc.), or is it more a book set in the same universe, but not directly a sequel?
I'm asking because in the first case I'll read it very quickly in order to remember accurately the details of the first book, but if it's just a book set in the same universe, I'll probably read a few books before reading this one, to return to this universe with a fresh eye.
(PS: Please don't post spoilers about the first book, as I'm not done reading it yet.)