DESY-HERA. Precise measurements of the spin structure functions and virtual photon asymmetries of the proton and deuteron over the kinematic range in X from 0.0041 to 0.9 and in Q**2 from 0.18 to 20 GeV**2. The data were collected in DIS of 27.6 GeV longitudinally polarized positrons from longitudinally polarized hydrogen and deuterium gas targets internal to the HERA ring. The neutron structure function is extracted by combining the proton and deuteron data. This part (1) contains the structure function and asymmetry measurements (part 2 contains the correlation matrices). DESY-HERA. Precise measurements of the spin structure functions and virtual photon asymmetries of the proton and deuteron over the kinematic range in X from 0.0041 to 0.9 and in Q**2 from 0.18 to 20 GeV**2. The data were collected in DIS of 27.6 GeV longitudinally polarized positrons from longitudinally polarized hydrogen and deuterium gas targets internal to the HERA ring. The neutron structure function is extracted by combining the proton and deuteron data. This part (2) contains the correlation matrices. (part 1 contains the structure functions and asymmetry measurements). ; Other ; Virtual photon asymmetries A1 for the proton and deuterium targets at the average values of X,and Q**2 in 15 bins. The first DSYS is the experimental uncertainty and includes the 5.2 (5.0) PCT normalization uncertainty for the proton (deuteron) data. The second DSYS systematic error is due to the uncertainty in the parameterizations (R, F2, A2, Azz, omegaD). The third DSYS systematic error is due to the uncertainty in evolving to a common Q**2.