We present the final results of a ROSAT PSPC program to study the soft X-ray emission properties of a complete sample of of low z quasars .
This sample includes all 23 quasars from the Bright Quasar Survey with z \leq 0.400 , and N _ { H~ { } I } ^ { \tiny Gal } < 1.9 \times 10 ^ { 20 } cm ^ { -2 } .
Pointed ROSAT PSPC observations were made for all quasars , yielding high S/N spectra for most objects which allowed an accurate determination of the spectral shape .
The following main results were obtained :

1 . The spectra of 22 of the 23 quasars are consistent , to within \sim 30 % , with a single power-law model at rest-frame 0.2 - 2 keV .
There is no evidence for significant soft excess emission with respect to the best fit power-law .
We place a limit ( 95 % confidence ) of \sim 5 \times 10 ^ { 19 } cm ^ { -2 } on the amount of excess foreground absorption by cold gas for most of our quasars .
The limits are \sim 1 \times 10 ^ { 19 } cm ^ { -2 } in the two highest S/N spectra .

2 . The mean 0.2 - 2 keV continuum of quasars agrees remarkably well with an extrapolation of the mean 1050Å-350Å continuum recently determined by Zheng et al .
( 1996 ) for z > 0.33 quasars .
This suggests that there is no steep soft component below 0.2 keV .

3 . Significant X-ray absorption ( \tau > 0.3 ) by partially ionized gas ( “ warm absorber ” ) in quasars is rather rare , occurring for \lesssim 5 % of the population , which is in sharp contrast to lower luminosity Active Galactic Nuclei ( AGNs ) , where significant absorption probably occurs for \sim 50 % of the population .

4 . Extensive correlation analysis of the X-ray continuum emission parameters with optical emission line parameters indicates that the strongest correlation is between the spectral slope \alpha _ { x } , and the H \beta FWHM .
A possible explanation for this remarkably strong correlation is a dependence of \alpha _ { x } on L / L _ { Edd } , as seen in Galactic black hole candidates .

5 . The strong correlations between \alpha _ { x } , and L _ { [ O~ { } III ] } , Fe II/H \beta , and the peak [ O III ] to H \beta flux ratio are verified .
The physical origin of these correlations is still not understood .

6 . There appears to be a distinct class of “ X-ray weak ” quasars , which form \sim 10 % of the population ( 3 out of 23 ) , where the X-ray emission is smaller by a factor of 10-30 than expected based on their luminosity at other bands , and on their H \beta luminosity .
These may be quasars where the direct X-ray source is obscured , and only scattered X-rays are observed .

7 . Thin accretion disk models can not reproduce the observed 0.2-2 keV spectral shape , and they also can not reproduce the tight correlation between the optical and soft X-ray emission .
An as yet unknown physical mechanism must be maintaining a strong correlation between the optical and soft X-ray emission .

8 . The H I/He I ratio in the high Galactic latitude ISM must be within 20 % , and possibly within 5 % , of the total H/He ratio of 10 , which indicates that He in the diffuse H II gas component of the interstellar medium is mostly ionized to He II or He III .

We finally note the intriguing possibility that although \langle \alpha _ { x } \rangle in radio-loud quasars ( -1.15 \pm 0.14 ) is significantly flatter than in radio-quiet quasars ( -1.72 \pm 0.09 ) the X-ray emission may not be related to the presence of radio emission .
The difference in \langle \alpha _ { x } \rangle may result from the strong \alpha _ { x } vs. H \beta FWHM correlation and the tendency of radio-loud quasars to have broader H \beta .