This paper details an investigation into Keplera??s Laws. Newtona??s technique for deducing an inverse-square law from Keplera??s Laws is given a modern presentation, with necessary background material included. Keplera??s Laws are then deduced from the assumption of an inverse-square law. This is done in a geometric style, inspired by Newtona??s work. Finally, a problem involving planetary orbits is stated and solved using the earlier results of the paper.