If "M" is an almost complex manifold, then its tangent bundle is a complex vector bundle. The Chern classes of "M" are thus defined to be the Chern classes of its tangent bundle. If "M" is also compact and of dimension 2"d", then each monomial of total degree 2"d" in the Chern classes can be paired with the fundamental class of "M", giving an integer, a Chern number of "M". If "M"′ is another almost complex manifold of the same dimension, then it is cobordant to "M" if and only if the Chern numbers of "M"′ coincide with those of "M".