Mesopotamia

Witch doctors (“ashipu”) worked seamlessly with physical healers (“asu”) in a mix of magic, religious imprecations, administration of salves and plasters, and surgical procedures. Practiced surgeons became revered teachers who drained infections, controlled bleeding, performed amputations and trephinations, and accepted liability for failed operations. The Law Code of Hammurabi  (c. 1700 BC) called for a surgeon’s hand to be cut off if the life of a person of high social order was lost as a result. Many of them specialized in the knowledge and the magic of particular anatomic spirits and therefore surgical areas of interest. They were the skilled technicians of the art of surgery who established the practical traditions that were passed on to Greeks.

Egypt

While the Babylonians were magicians and generalists, the Egyptian physician-surgeons became specialists, some concentrating on the head, others eyes, yet others on the abdomen. They had extensive knowledge of anatomy, and performed dissections as well as mummification. They performed trephinations as early as 8000 BC.
The word “brain” was first observed in Edwin Smith Papyrus in 1700 BC. The convolutions of the freshly dissected brain surface were compared to “molten copper” when they were seen shining in the hot Egyptian sun.

Egyptian surgical instruments were some of the most sophisticated to be found until well after the Middle Ages.