Einstein’s field equations in the light of constrained hyperbolic systems

Results previously known in the literature, on the hyperbolicity of Einstein’s equations, are here quoted and improved. This aim is reached by applying recent techniques on constrained hyperbolic systems. The symmetric hyperbolic form is obtained, also in the four-dimensional formalism using harmonic coordinates. The case of sources due to the presence of matter is also considered, in particular from the view point of Extended Thermodynamics.