We present the results of an analysis of our infrared light curves of the Algol-type binary AI Draconis in the J, H and K bands, and of published light curves in the B, V and Strömgren uvby bands, together with spectra obtained by us. The analysis of the light curves was carried out using a code based on ATLAS model atmospheres and Roche geometry. The small contribution of the secondary cool component to the total light of the system in the visible, producing light curves with very shallow secondary eclipses, makes the stellar and orbital parameters derived from light-curve analysis in the visible spectral range uncertain. The larger contribution of the secondary star to the infrared fluxes makes this range particularly well suited to the derivation of precise orbital and stellar parameters in binaries of Algol type. From the simultaneous solution of the infrared JHK light curves, we derive the following absolute orbital and stellar parameters for the two components: = 10160 +/- 160 K, Req,1= 2.12 +/- 0.04 Rsolar, log()1= 4.23; = 5586 +/- 110 K, Req,2= 2.36 +/- 0.04 Rsolar, log()2= 3.76; M1= 2.86 +/- 0.09 Msolar, q=M2/M1= 0.44 +/- 0.03; a= 7.62 +/- 0.09 Rsolar, i= 76.53°+/- 0.3°, e~= 0.0. Here, and log() indicate average surface values, Req is the equivalent radius of the deformed star and a is the orbital size. In our light-curve solutions, the secondary star of AI Dra fills its Roche lobe (as also indicated by the spectroscopy), thus discounting claims, based on UBV light curves, that both components of the binary are located within their Roche lobes. The visible and infrared photometry show no evidence of any significant infrared excess in the system, and the distance of AI Dra is estimated as d= 169 +/- 17 pc. Based on the spectra of AI Dra and template stars in the ranges 8210-9060, 6250-7130 and 4040-4920 Å, we classify the stellar components of AI Dra and find that the most probable spectral types are A0V (or perhaps A1V) for the primary and F9.5V for the secondary (although it could reach as far as G4V), respectively. From our spectroscopic observations, the spectral evolution of AI Dra with orbital phase is also presented. Furthermore, we obtain the projected rotational velocity of the secondary, whose value turns out to be compatible with the star filling its Roche lobe.