What can we learn from the neural networks of C.elegans to understand human brains? Recently I am reading some works about Caenorhabditis Elegans. A C.elegans has 302 neurons and we already know the function and connection of every one of their neurons so that we can exactly reconstruct it by computer programs. Also, C.elegans have a couple of sensory inputs, and a kind of intelligence (they can learn something).

The question is: what can we learn from C.elegans, so that we can understand Human brains?

To specify, I want to know:


What's the relationship between C.elegans and Human beings (or primates)? Is there any route in the terms of evolution?
Does the neural system of C.elegans still exist in human brains, as either a working or an idle part? 


I am a computer scientist working on artificial intelligence. My purpose is to clarify the mechanisms of the Human brain. I hope C.elegans could help but I don't know much about biology.
Caenorhabditis elegans is probably not an ancestor to Humans. As found in Sponge proteins are more similar to those of Homo sapiens than to Caenorhabditis elegans, certain sponges were found to have more similar protein structures to humans than C. elegans suggesting the sponges are the ancestor. 

For your second point, it depends what you mean. The actual, exact sort of network in C. elegans doesn't exist as a "part" in Human brains nor would it even if humans had C elegans as a direct ancestor; the network would have evolved considerably. 

The basic structure of the neural network as a connected net of neurons and the basic functionality has of course remained through all organisms with developed neural networks. Like all life, certain related developmental processes exist between humans and C. elegans, which is why studying them (and most any other animal) is often relevant to Human research of similar biological or psychological areas of interest.

C. elegans can even learn, showing it is a very complete model of a neural network, despite it's simplicity.

C. elegans is not studied because it is an ancestor or because it has any particular relation to the human mind, but because it has an extremely simple, completely functional neural network. There are complete maps of C elegans' neural network and even online tools to search the synapses of C elegans. There are whole websites dedicated to research on C. elegans.

Similar to fruit flies, C. elegans also provide a great vector for developmental research because they have a lifespan of a couple weeks instead of decades.

Some great further reading is the introductory Why use C. elegans to study the synapse ?