The main topic of classical knot theory is the classification of knots and links with equivalence. In this thesis we classify knots by arc index. Every knot can be embedded in the union of finitely many half planes with a common boundary line in such a way that the portion of the knot in each half plane is a properly embedded arc. The minimal number of such half planes is called the arc index of the knot. We introduce the methods that the author obtained the list of prime knots with arc index up to 11. By using computers, we obtained 663,341 Cromwell matrices and converted to dowker codes. First we obtained lists of prime knots with crossing number up to 16. Next we investigate all computable invariants of prime knots with 17-24 crossings and we use a knotplot program to distinguish them.
Also we prove that the arc index of a nonsplit non-alternating prime knot is not bigger than the crossing number.