We present the first GALEX UV images of the well known interacting group of galaxies , Stephan ’ s Quintet ( SQ ) . We detect widespread UV emission throughout the group . However , there is no consistent coincidence between UV structure and emission in the optical , H \alpha , or HI . Excluding the foreground galaxy NGC 7320 ( Sd ) , most of the UV emission is found in regions associated with the two spiral members of the group , NGC 7319 and NGC 7318b , and the intragroup medium starburst SQ-A . The extinction corrected UV data are analyzed to investigate the overall star formation activity in SQ . It is found that the total star formation rate ( SFR ) of SQ is 6.69 \pm 0.65 M _ { \sun } yr ^ { -1 } . Among this , 1.34 \pm 0.16 M _ { \sun } yr ^ { -1 } is due to SQ-A . This is in excellent agreement with that derived from extinction corrected H \alpha luminosity of SQ-A . The SFR in regions related to NGC 7319 is 1.98 \pm 0.58 M _ { \sun } yr ^ { -1 } , most of which ( 68 % ) is contributed by the disk . The contribution from the ’ young tail ’ is only 15 % . In the UV , the ’ young tail ’ is more extended ( \sim 100 kpc ) and shows a loop-like structure , including the optical tail , the extragalactic HII regions recently discovered in H \alpha , and other UV emission regions discovered for the first time . The UV and optical colors of the ’ old tail ’ are consistent with a single stellar population of age t \simeq 10 ^ { 8.5 \pm 0.4 } yrs . The UV emission associated with NGC 7318b is found in a very large ( \sim 80 kpc ) disk , with a net SFR of 3.37 \pm 0.25 M _ { \sun } yr ^ { -1 } . Several large UV emission regions are 30 — 40 kpc away from the nucleus of NGC 7318b . Although both NGC 7319 and NGC 7318b show peculiar UV morphology , their SFR is consistent with that of normal Sbc galaxies , indicating that the strength of star formation activity is not enhenced by interactions .