  We show how the recently again discussed $N$-point Witt, Virasoro, and affine
Lie algebras are genus zero examples of the multi-point versions of
Krichever--Novikov type algebras as introduced and studied by Schlichenmaier.
Using this more general point of view, useful structural insights and an easier
access to calculations can be obtained. The concept of almost-grading will
yield information about triangular decompositions which are of importance in
the theory of representations. As examples the algebra of functions, vector
fields, differential operators, current algebras, affine Lie algebras, Lie
superalgebras and their central extensions are studied. Very detailed
calculations for the three-point case are given.
