  We describe some regular techniques of calculating finite degree invariants
of triple points free smooth plane curves $S^1 \to R^2$. They are a direct
analog of similar techniques for knot invariants and are based on the calculus
of {\em triangular diagrams} and {\em connected hypergraphs} in the same way as
the calculation of knot invariants is based on the study of chord diagrams and
connected graphs.
  E.g., the simplest such invariant is of degree 4 and corresponds to the
diagram consisting of two triangles with alternating vertices in a circle in
the same way as the simplest knot invariant (of degree 2) corresponds to the
2-chord diagram $\bigoplus$. Also, following V.I.Arnold and other authors we
consider invariants of {\em immersed} triple points free curves and describe
similar techniques also for this problem, and, more generally, for the
calculation of homology groups of the space of immersed plane curves without
points of multiplicity $\ge k$ for any $k \ge 3.$
