Self-intersection surfaces, regular homotopy, and finite order invariants

Explicit formulas for the regular homotopy classes of generic immersions $S^k\to{\mathbb R}^{2k-2}$ are given in terms of the corresponding self-intersection manifolds with natural additional structures.
There is a natural notion of finite order invariants of generic immersions. We determine the group of $m$th order invariants for each $m$ and prove that the finite order invariants are not sufficient for distinguishing generic immersions that cannot be obtained from each other by a regular homotopy through generic immersions.