There are so many traditions on Inauguration Day, but only one is required by law, and that is saying the Oath of Office. Taking the Oath with your hand on a book According to the U.S. Department of State,

The tradition of using a Bible during the swearing-in goes back to the very first inauguration, but not all Presidents have used one.

Trump was sworn in as the 47th president of the United States on Monday, taking the oath without placing his hand on the Bible