We present the first fully and uniformly sampled , spatially complete H i survey of the entire Magellanic System with high velocity resolution ( \Delta v = 1.0 km s ^ { -1 } ) , performed with the Parkes Telescope The Parkes Telescope is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO . Approximately 24 percent of the southern sky was covered by this survey on a \approx 5′ grid with an angular resolution of HPBW = 14 \aas@@fstack { \prime } 1 . A fully automated data-reduction scheme was developed for this survey to handle the large number of H i spectra ( 1.5 \times 10 ^ { 6 } ) . The individual Hanning smoothed and polarization averaged spectra have an rms brightness temperature noise of \sigma = 0.12 K. The final data-cubes have an rms noise of \sigma _ { rms } \approx 0.05 K and an effective angular resolution of \approx 16′ . In this paper we describe the survey parameters , the data-reduction and the general distribution of the H i 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 H i mass of M ( H i ) = 4.87 \cdot 10 ^ { 8 } M _ { \odot } \left [ d / 55 ~ { } { kpc } \right ] ^ { 2 } , if all H i gas is at the same distance of 55 kpc . Approximately two thirds of this H i gas is located close to the Magellanic Clouds ( Magellanic Bridge and Interface Region ) , and 25 % of the H i gas is associated with the Magellanic Stream . The Leading Arm has a four times lower H i mass than the Magellanic Stream , corresponding to 6 % of the total H i 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 H i 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 H i 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 .