Fibers found in a cave have been carbon dated to 34,000 years ago. Some of the fibers were twisted, indicating they were used to make ropes or strings. Others had been dyed. Learn more by clicking this link: Archaeologists Discover Oldest-known Fiber Materials Used By Early Humans ( via Science Daily).
I volunteer in the Science Museum of Minnesota's Collections Gallery. I often watch Mary Johnson demonstrate spinning wool into string and Dick Enstead spinning string into rope.