Short answers, pulled from the story.
The nervous system is the highly complex part of an animal that coordinates its actions and sensory information by transmitting signals to and from different parts of its body. It detects environmental changes and works in tandem with the endocrine system to respond. In vertebrates it consists of the central nervous system and the peripheral nervous system.
Nervous tissue first arose in wormlike organisms about 550 to 600 million years ago. The common bilaterian ancestor appears as fossils beginning in the Ediacaran period. All bilateria are thought to have descended from this wormlike ancestor.
A neuron is the special cell that defines nervous tissue, distinguished by communicating with other cells through synapses. Many neurons possess an axon, a protrusion that can extend to distant parts of the body and make thousands of synaptic contacts. Even within humans, hundreds of different types of neuron exist.
In Caenorhabditis elegans, males have exactly 383 neurons while hermaphrodites have exactly 302 neurons. Its nervous system is sexually dimorphic and has been completely mapped into a connectome including its synapses. Because every neuron is uniquely identifiable, the nervous system is specified entirely by the genome.
A Mauthner cell is a gigantic identified neuron in fish, the best known identified neuron in vertebrates. Every fish has two Mauthner cells in the bottom part of the brainstem, one on the left and one on the right. A single action potential makes the fish curve into a C-shape within milliseconds as a fast escape response.
The fastest nerve signals travel at speeds that exceed 100 meters per second. The nervous system uses point-to-point signalling, with neurons projecting axons to specific targets. This makes neural signalling both more specific and much faster than hormonal signalling.
Long-term potentiation, abbreviated LTP, is the best-known form of neural memory, discovered in 1973. It operates at synapses that use glutamate acting on the NMDA receptor, where simultaneous activation lets calcium flow into the target cell and strengthen the synapse. This change in strength can last for weeks or longer.