There are 20 districts called "Arrondissements". The first of them is in the very center of the city. From there on, they are arranged in a clockwise outwardly moving spiral.
The river Seine divides Paris into left bank ("Rive Gauche") and right bank ("Rive Droite"). Both terms are used by Parisians to characterise their residents: left bank means artsy, bohemian and intellectual; right bank conservative, elegant and business-oriented.
The two islands in the Seine – "Île de la Cité" and "Île Saint-Louis" – are landmarks on their own. Many of the popular sights like Notre-Dame cathedral are located in this area.
On paper, Paris stops where the 20 districts end. Huge areas, that seem to be part of the city – like the notorious Banlieue suburbs and the impressive office district La Defense – are actually outside of the official borders.