The curves on an algebraic variety control to a remarkable degree the structure of the variety: The closed cone of curves is dual to the cone of nef divisors, so knowing about curves can give information about nef divisors. Mori's Cone Theorem gives strong restrictions on the shape of the closed cone of curves and consequently gives powerful information about the structure of a variety.
In this talk, I will begin by defining the closed cone of curves and then prove the duality between the clsoed cone of curves and the cone of nef divisors. I will explain the statement of the cone theorem. Finally, I will illustrate the cone of curves with examples, and I will end by running out of time.