Polynomial knot theory is similar to holonomic knot theory
except that here we have non compact knots. It is well known that every
knot-type has a representative given by a polynomial embedding from ${\bf R}
$ to ${\bf R}^3$ which is unique up to {\it polynomial isotropy}. We will
discuss the motivation behind the polynomial representation of knots and
try to see some methods to explicitly construct polynomial representation
for few classes of knots.