Who wrote the book "al umm al Shafi'i"

"al umm al Shafi'i" is a book attributed to imam al Shafi'i. But everything in the book is "al shafi'i said: ...." so clearly he himself did not write the book. Some articles say it was dictated to his student. But that can't be true either because in many parts of the book al shafi'i is the second or third person in a chain. for example: أَخْبَرَنَا الرَّبِيعُ قَالَ أَخْبَرَنَا الشَّافِعِيُّ So who really wrote this book? thanks