  In this paper we construct new invariants of knotoids including the odd
writhe, the parity bracket polynomial, the affine index polynomial and the
arrow polynomial, and give an introduction to the theory of virtual knotoids.
The invariants in this paper are defined for classical knotoids in analogy to
corresponding invariants of virtual knots. The affine index polynomial and the
arrow polynomial provide bounds on the height (minimum crossing distance
between endpoints) of a classical knotoid. We show that classical knotoids have
symmetric affine index polynomials.
