The AMADEUS (ANTARES Modules for the Acoustic Detection Under the Sea) system which is described in this article aims at the investigation of techniques for acoustic detection of neutrinos in the deep sea. It is integrated into the ANTARES neutrino telescope in the Mediterranean Sea. Its acoustic sensors, installed at water depths between 2050 and 2300 m, employ piezo-electric elements for the broad-band recording of signals with frequencies ranging up to 125 kHz. The typical sensitivity of the sensors is around - 145 dB re 1 V/mu Pa (including preamplifier). Completed in May 2008, AMADEUS consists of six 'acoustic clusters', each comprising six acoustic sensors that are arranged at distances of roughly 1 m from each other. Two vertical mechanical structures (so-called lines) of the ANTARES detector host three acoustic clusters each. Spacings between the clusters range from 14.5 to 340 m. Each cluster contains custom-designed electronics boards to amplify and digitise the acoustic signals from the sensors. An on-shore computer cluster is used to process and filter the data stream and store the selected events. The daily volume of recorded data is about 10 GB. The system is operating continuously and automatically, requiring only little human intervention. AMADEUS allows for extensive studies of both transient signals and ambient noise in the deep sea, as well as signal correlations on several length scales and localisation of acoustic point sources. Thus the system is excellently suited to assess the background conditions for the measurement of the bipolar pulses expected to originate from neutrino interactions.