We report the first radar soundings of the ionosphere of Mars with the MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding) instrument on board the orbiting Mars Express spacecraft. Several types of ionospheric echoes are observed, ranging from vertical echoes caused by specular reflection from the horizontally stratified ionosphere to a wide variety of oblique and diffuse echoes. The oblique echoes are believed to arise mainly from ionospheric structures associated with the complex crustal magnetic fields of Mars. Echoes at the electron plasma frequency and the cyclotron period also provide measurements of the local electron density and magnetic field strength.