This contribution presents results of comprehensive investigation of the E-H transition in an inductively coupled radio frequency argon/oxygen discharge at 13.56 MHz. For the characterization of the discharge arrangement, the spatial magnetic and electric field components of the planar coil in vacuum are calculated and provide information about the electron heating region. The used double coil leads to a radial symmetric field distribution. Further, voltage and current probe measurements reveal the inductivity of the coil and the phase shift between the coil voltage and the current. As a result, the coil current and the RF voltage are directly proportional. The phase shift is nearly constant in the E-mode and decreases slightly in the H-mode. The positive ion saturation current as well as the line integrated electron density are measured by means of Langmuir probe and 160 GHz microwave interferometer, respectively, to study the mode transition in argon with different oxygen contents. The positive ion saturation current and the electron density decrease with increasing oxygen admixture at fixed pressure and RF power. The onset and the way of the E-H transition strongly depend on the oxygen content. The mode transition of a pure argon discharge is step like and changes to a continuous mode transition with the admixture of oxygen.