For every field extension L/K, one has a restriction map res = res(L/K) : B(K) -> B(L) of Brauer groups, sending a Brauer class {[}A] to {[}A circle times(K) L]. (So actually, res is extension of scalars; it is called restriction by virtue of the cohomological description of Brauer groups; cf. Gruenberg, 1967, p. 125). The kernel of res is denoted B(L/K) and is called the relative Brauer group of the extension. In the case of global. elds, B(L/K) has been determined in Fein et al. (1981). If L/K is separable, one also has a corestriction map B(L) -> B(K), cf. Kersten (1990, 18). The purpose of the present note is to derive information on the kernel and cokernel of both maps in the number field case by making full use of Hasse's ``Main Theorem in the Theory of Algebras{''}.