Rotating Black Holes in Higher Dimensions with a Cosmological Constant

We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and the Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated $S^{D-2}$ bundles over $S^2$, infinitely many for each odd $D\ge 5$. Applications to string theory and M-theory are indicated.