3 Answers

Surgery is the branch of medicine that deals with the physical manipulation of a bodily structure to diagnose, prevent, or cure an ailment. Ambroise Paré, a 16th century French surgeon, stated that there were to perform surgery: "To eliminate that which is superfluous, restore that which has been dislocated, separate that which has been united, join that which has been divided and repair the defects of nature."
Since humans first learned to make and handle tools, they have employed their talents to develop surgical techniques, each time more sophisticated than the last; however, until the industrial revolution, surgeons were incapable of overcoming the three principal obstacles which had plagued the medical profession from its infancy — bleeding, pain and infection. Advances in these fields have transformed surgery from a risky "art" into a scientific discipline capable of treating many diseases and conditions.

Read more >http://en.wikipedia.org/wiki/History_of_surgery

The name was Sushruta (  around 800BC) He was an ancent Indian Surgein and is the author of a book ,Sushruta Samhita.

Difficult to say who because we have to know time,place and type of surgery. What we do know is that humans have been surgeons starting small things in body. As science progressed, the process of surgery got formalized and continues to be refined.