It's Brain Surgery right?
Yes, but also much more - neurosurgeons do operate on the brain but also on the spine, back and peripheral nerves.
The clinical definition states:  Neurosurgery is the medical specialty concerned with the prevention, diagnosis, treatment and rehabilitation of disorders that affect the entire nervous system including the spinal column, spinal cord, brain and peripheral nerves.

For a listing & descriptions of conditions & treatments a neurosurgeon regularly treats click here.

So a neurosurgeon can do my back surgery?

Yes, a neurosurgeon or a orthopaedic surgeon can do back surgery. Some neurosurgeons specialist in brain surgery and have do some spinal surgery, and some orthopaedic surgeons do mostly joint surgery and some spinal surgery.   It is important to consult with one or both to determine which will be a better choice.