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EURECA (EURopean-JapanEse Calorimeter Array) comprises a 5 x 5 pixel imaging TES-based micro-calorimeter array read-out by SQUID-based frequency-domain-multiplexed electronics and cooled down by an adiabatic demagnetization refrigerator. A European-Japanese consortium designs, fabricates, and tests this prototype instrument with the aim to show within about 2 years technology readiness of a TES-based X-ray imaging micro-calorimeter array in anticipation of future X-ray astronomy missions, like XEUS (ESA), Constellation-X (NASA), NEXT (JAXA), DIOS (JAXA), ESTREMO (ASI), and NEW (Dutch-multinational). This paper describes the instrument concept, and shows the design of the various sub-units, like the TES detector array, LC-filters, SQUID-amplifiers, flux-locked-loop electronics, AC-bias sources, etc.