Abstract. We present a statistical study of four years of Cluster crossings of the mid-altitude cusp. In this first part of the study, we start by introducing the method we have used a) to define the cusp properties, b) to sort the interplanetary magnetic field (IMF) conditions or behaviors into classes, c) to determine the proper time delay between the solar wind monitors and Cluster. Out of the 920 passes that we have analyzed, only 261 fulfill our criteria and are considered as cusp crossings. We look at the size, location and dynamics of the mid-altitude cusp under various IMF orientations and solar wind conditions. For southward IMF, B_z rules the latitudinal dynamics, whereas B_y governs the zonal dynamics, confirming previous works. We show that when |B_y| is larger than |B_z|, the cusp widens and its location decorrelates from B_y. We interpret this feature in terms of component reconnection occurring under B_y-dominated IMF. For northward IMF, we demonstrate that the location of the cusp depends primarily upon the solar wind dynamic pressure and upon the Y-component of the IMF. Also, the multipoint capability of Cluster allows us to conclude that the cusp needs typically more than ~20 min to fully adjust its location and size in response to changes in external conditions, and its speed is correlated to variations in the amplitude of IMF-B_z. Indeed, the velocity in °ILAT/min of the cusp appears to be proportional to the variation in B_z in nT: V_cusp=0.024 ΔB_z. Finally, we observe differences in the behavior of the cusp in the two hemispheres. Those differences suggest that the cusp moves and widens more freely in the summer hemisphere.