The outer membrane that covers the brain is

The outer membrane that covers the brain is called the "dura mater". It is a thick, tough, and fibrous layer that provides protection and support to the brain. The dura mater is the outermost layer of the three meninges (the protective membranes that surround the brain and spinal cord). It lies closest to the skull and forms a barrier that separates the brain from the bones of the skull. The dura mater contains blood vessels and nerves that supply the brain and is responsible for anchoring the brain in place.