Electro Discharge Machining (EDM) is a non-contact technique allowing machining of electricallyconductive materials; it is well adapted for the machining of hard materials. The principle is based onthe creation of eroding electrical discharges between a tool and a piece, both immersed in adielectric. In this thesis, we have the studied miniaturization of the process, called micro electrodischarge machining (μ-EDM), which is considered as a complementary technique of mechanical orlaser micro-machining techniques and silicon micro technology processes (RIE, DRIE, LIGA)..However, the resolution of μEDM is limited.In this work, we have firstly developed an original method for making tungsten micro-tools withcylindrical profile by electrochemical etching. This method allows the reproducible fabrication ofmicro-tool with 15-μm diameter. Thinner micro-tools were also obtained (down to 700 nm) withreproducibility problems. Furthermore, a prototype machine for milling μ-EDM was developed with afully characterized electronics. Micro channels were obtained respectively in stainless steel with awidth of 40μm and in titanium with a width of 25μm; a surface roughness Ra of 86 nm was achievedin 600 x 600 x 30 μm cavities. Besides, the limitations of the apparatus were highlighted. In the lastpart of this work, we have studied the micro-discharge and the micro-plasma between the micro-tooland the part with electrical characterization. The resistivity and the inductance of the sparks weremeasured and integrated in a numerical model in order to explain the duration of the microdischarges and their intensity. Solutions for improving the machining resolution are also discussed atthe end of this work.