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Using a method to correct redshift space distortion (RSD) for individualgalaxies, we mapped the real space distributions of galaxies in the SloanDigital Sky Survey (SDSS) Data Release 7 (DR7). We use an ensemble of mockcatalogs to demonstrate the reliability of our method. Here as the first paperin a series, we mainly focus on the two point correlation function (2PCF) ofgalaxies. Overall the 2PCF measured in the reconstructed real space forgalaxies brighter than $^{0.1}{\rm M}_r-5\log h=-19.0$ agrees with the directmeasurement to an accuracy better than the measurement error due to cosmicvariance, if the reconstruction uses the correct cosmology. Applying the methodto the SDSS DR7, we construct a real space version of the main galaxy catalog,which contains 396,068 galaxies in the North Galactic Cap with redshifts in therange $0.01 \leq z \leq 0.12$. The Sloan Great Wall, the largest knownstructure in the nearby Universe, is not as dominant an over-dense structure asappears to be in redshift space. We measure the 2PCFs in reconstructed realspace for galaxies of different luminosities and colors. All of them show cleardeviations from single power-law forms, and reveal clear transitions from1-halo to 2-halo terms. A comparison with the corresponding 2PCFs in redshiftspace nicely demonstrates how RSDs boost the clustering power on large scales(by about $40-50\%$ at scales $\sim 10 h^{-1}{\rm {Mpc}}$) and suppress it onsmall scales (by about $70-80\%$ at a scale of $0.3 h^{-1}{\rm {Mpc}}$).

Mapping the real space distributions of galaxies in SDSS DR7: I. Two Point Correlation Functions