  General Relativity theory is reviewed following the vierbein field theory
approach proposed in 1928 by Einstein. It is based on the vierbein field taken
as the "square root" of the metric tensor field. Einstein's vierbein theory is
a gauge field theory for gravity; the vierbein field playing the role of a
gauge field but not exactly like the vector potential field does in Yang-Mills
theory--the correction to the derivative (the covariant derivative) is not
proportional to the vierbein field as it would be if gravity were strictly a
Yang-Mills theory. Einstein discovered the spin connection in terms of the
vierbein fields to take the place of the conventional affine connection. To
date, one of the most important applications of the vierbein representation is
for the derivation of the correction to a 4-spinor quantum field transported in
curved space, yielding the correct form of the covariant derivative. Thus, the
vierbein field theory is the most natural way to represent a relativistic
quantum field theory in curved space. Using the vierbein field theory,
presented is a derivation of the the Einstein equation and then the Dirac
equation in curved space. Einstein's original 1928 manuscripts translated into
English are included.
