From the author's abstract ``It is proved that there exist metrics with holonomy \(G_ 2\) and Spin(7), thus settling the remaining cases in Berger's list of possible holonomy groups. We first reformulate the ``holonomy H'' condition as a set of differential equations for an associated H-structure on a given manifold. We collect the needed algebraic facts about \(G_ 2\) and Spin(7). We then apply the machinery of over-determined partial differential equations (in the form of the Cartan-Kähler theorem) to prove the existence of solutions whose holonomy is \(G_ 2\) or Spin(7). We also provide explicit examples and some information about the ``generality'' of the space of such metrics.'' Moreover, the explicit examples given in section 5, are cones on homogeneous spaces. For example, to settle the \(G_ 2\) case, the author shows that the normal SU(3)-invariant metric on \(SU(3)/T^ 2\), \(T^ 2\) a maximal torus, gives rise to a cone metric on \(R^+\times (SU(3)/T^ 2)\) with holonomy \(G_ 2\). An analogous construction is used in the Sp(7) case.