  We discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of U(N)
instantons in noncommutative (NC) space and prove the one-to-one correspondence
between moduli spaces of the noncommutative instantons and the ADHM data,
together with an origin of the instanton number for U(1). We also give a
derivation of the ADHM construction from the viewpoint of the Nahm
transformation of instantons on four-tori. This article is a composite version
of [23] and [24].
