  The paper introduces Slope Conjecture which relates the degree of the Jones
polynomial of a knot and its parallels with the slopes of incompressible
surfaces in the knot complement. More precisely, we introduce two knot
invariants, the Jones slopes (a finite set of rational numbers) and the Jones
period (a natural number) of a knot in 3-space. We formulate a number of
conjectures for these invariants and verify them by explicit computations for
the class of alternating knots, torus knots, the knots with at most 9
crossings, and the $(-2,3,n)$ pretzel knots.
