  In this paper we introduce and study $n$-point Virasoro algebras,
$\tilde{\W_a}$, which are natural generalizations of the classical Virasoro
algebra and have as quotients multipoint genus zero Krichever-Novikov type
algebras. We determine necessary and sufficient conditions for the latter two
such Lie algebras to be isomorphic. Moreover we determine their automorphisms,
their derivation algebras, their universal central extensions, and some other
properties. The list of automorphism groups that occur is $C_n$, $D_n$, $A_4$,
$S_4$ and $A_5$. We also construct a large class of modules which we call
modules of densities, and determine necessary and sufficient conditions for
them to be irreducible.
