Order one invariants of immersions of surfaces into 3-space

We classify all order one invariants of immersions of a closed orientable surface F into ℝ³, with values in an arbitrary Abelian group G. We show that for any F and G and any regular homotopy class A of immersions of F into ℝ³, the group of all order one invariants on A is isomorphic to double strok G sign^א0 ⊕ double strok B sign ⊕ double strok B sign where double strok G sign^א0 is the group of all functions from a set of cardinality א0 into double strok G sign and double strok B sign = {x ∈ double strok G sign : 2x = 0}. Our work includes foundations for the study of finite order invariants of immersions of a closed orientable surface into ℝ³, analogous to chord diagrams and the 1-term and 4-term relations of knot theory.