High-resolution far-infrared and sub-millimetre spectroscopy of water lines is an important tool to understand the physical and chemical properties of cometary atmospheres. We present observations of several rotational ortho- and para-water transitions in comet C/2008 Q3 (Garradd) performed with HIFI on Herschel. These observations have provided the first detection of the 2(12)-1(01) (1669 GHz) ortho and 1(11)-0(00) (1113 GHz) para transitions of water in a cometary spectrum. In addition, the ground-state transition 1(10)-1(01) at 557 GHz is detected and mapped. By detecting several water lines quasi-simultaneously and mapping their emission we can constrain the excitation parameters in the coma. Synthetic line profiles are computed using excitation models which include excitation by collisions, solar infrared radiation, and radiation trapping. We obtain the gas kinetic temperature, constrain the electron density profile, and estimate the coma expansion velocity by analyzing the map and line shapes. We derive water production rates of 1.7-2.8 x 10(28) s(-1) over the range r(h) = 1.83-1.85 AU.