Which one is grammatically correct?
"Together with Rudolf and Friedrich I wrote this book."
"Together with Rudolf and Friedrich we wrote this book."
Which one is grammatically correct?
"Together with Rudolf and Friedrich I wrote this book."
"Together with Rudolf and Friedrich we wrote this book."
Both the sentences are correct grammatically.
The phrase together with is used in the same pattern as in addition to, besides, and along with; it doesn't alter the subject of a sentence.
In the latter, the subject "we" indicates that in addition to me there's another person or more persons who wrote this book, of course; Rudolf and Freidrich are not included in 'we'.
If forced to pick, I would say "Together with ... I wrote this book."
But as you can tell it's an awkward sentence. It feels odd to give credit to two other people, who helped to some unknown degree, and then apparently claim that you wrote it. It leaves the reader with unanswered and distracting questions.
On the other hand, "together with ... we" is wrong because it's missing the first-person pronoun in the sentence. You need to include yourself somewhere if you want to use the "we".
Some better ways to phrase this:
I wrote this book with the help of Rudolf and Friedrich.
This book is a collaboration between Rudolf, Friedrich, and myself.
Rudolf, Friedrich, and I wrote this book together.