How does the embryo turn from gastrula into neurula? How is the neural tube formed? What is the embryonic origin of the nervous system in vertebrates?

The neurula stage is divided by the appearance of the neural tube along the dorsal region of the embryo. The growth of mesoderm in that region induces the differentiation of ectodermal cells just above. These cells then distinguish forming the neural tube. So the origin of the nervous system is the ectoderm (the similar germ layer that gives birth to the skin).