We present the first fully and uniformly sampled, spatially complete survey of the entire Magellanic System with high velocity resolution ( km s -1), performed with the Parkes Telescope. Approximately 24 percent of the southern sky was covered by this survey on a 5´ grid with an angular resolution of . A fully automated data-reduction scheme was developed for this survey to handle the large number of spectra ( ). The individual Hanning smoothed and polarization averaged spectra have an rms brightness temperature noise of = 0.12 K. The final data-cubes have an rms noise of K and an effective angular resolution of 16´. In this paper we describe the survey parameters, the data-reduction and the general distribution of the gas. The Large Magellanic Cloud ( LMC ) and the Small Magellanic Cloud ( SMC ) are associated with huge gaseous features - the Magellanic Bridge , the Interface Region , the Magellanic Stream , and the Leading Arm - with a total mass of M( ) = , if all gas is at the same distance of 55 kpc. Approximately two thirds of this gas is located close to the Magellanic Clouds ( Magellanic Bridge and Interface Region ), and 25% of the gas is associated with the Magellanic Stream . The Leading Arm has a four times lower mass than the Magellanic Stream , corresponding to 6% of the total mass of the gaseous features. We have analyzed the velocity field of the Magellanic Clouds and their neighborhood introducing a LMC-standard-of-rest frame. The in the Magellanic Bridge shows low velocities relative to the Magellanic Clouds suggesting an almost parallel motion, while the gas in the Interface Region has significantly higher relative velocities indicating that this gas is leaving the Magellanic Bridge building up a new section of the Magellanic Stream . The Leading Arm is connected to the Magellanic Bridge close to an extended arm of the LMC . The clouds in the Magellanic Stream and the Leading Arm show significant differences, both in the column density distribution and in the shapes of the line profiles. The gas in the Magellanic Stream is more smoothly distributed than the gas in the Leading Arm . These morphological differences can be explained if the Leading Arm is at considerably lower z-heights and embedded in a higher pressure ambient medium.