  We discuss instantons on noncommutative four-dimensional Euclidean space. In
commutative case one can consider instantons directly on Euclidean space, then
we should restrict ourselves to the gauge fields that are gauge equivalent to
the trivial field at infinity. However, technically it is more convenient to
work on four-dimensional sphere.
  We will show that the situation in noncommutative case is quite similar. One
can analyze instantons taking as a starting point the algebra of smooth
functions vanishing at infinity, but it is convenient to add a unit element to
this algebra (this corresponds to a transition to a sphere at the level of
topology). Our approach is more rigorous than previous considerations ; it
seems that it is also simpler and more transparent. In particular, we obtain
the ADHM equations in a very simple way.
