This is my first book of poetry working with you, so I hope this will eventually be the first step to a long partnership.
I got this from my American buddy, but this is weird to me. Is he making a stupid mistake? Or am I stupid?
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This is not incorrect, and no one would have any difficulty understanding you.
On the other hand, I think it's a little clumsy, and not just because of the bland verb choice "working". I would say
This is the first time I have had the opportunity to write a book of poetry with you, but I hope this will eventually be the first step in a long partnership.
I'm not seeing a mistake there. It may be clearer with a different verb there:
This is my first book collaborating with you, so I hope this will eventually be the first step to a long partnership.
"Collaborating" and "working" are interchangable here.
He's just saying that this book was his first time working with you, and that he hopes it is the first step to a long partnership of more collaboration.