What is the name of the part of the nervous system that includes all of the nerves, each of which is composed of bundles of neurons carrying messages toward and away from the brain and spinal cord?

The correct answer is the peripheral nervous system.

In vertebrates, there are two main parts of the nervous system, that is, the central nervous system and the peripheral nervous system. The central nervous system comprises of the spinal cord and the brain.

On the other hand, the peripheral nervous system comprises basically of nerves that are bounded bundles of axons or long fibers, which associate the central nervous system to each part of the body.