In short: YUP!
The man William Shakespeare – actor, poet, son of a prominent family in Stratford-upon-Avon, husband of Anne Hathaway, and member of the Lord Chamberlain’s Men – certainly collaborated with other writers, had his plays stolen out from under him by printers and actors looking to make a quick buck, and was much more interested in publishing poetry than scripts, but there’s no reason to doubt that he was the primary writer of these works. If you’d like to learn more, click here to read Isaac Butler’s excellent article “Shakespeare was Shakespeare.”
In the end, we at Seattle Shakespeare prefer to focus on the works of William Shakespeare and how they have been coming to life in the hands of artists around the world for centuries.