Measurements of diffractive dissociation cross sections in pp collisions at root s = 7 TeV are presented in kinematic regions defined by the masses M-X and M-Y of the two final-state hadronic systems separated by the largest rapidity gap in the event. Differential cross sections are measured as a function of xi= M-X(2)/s in the region -5.5 < log(10)xi 10(X) < -2.5, for logio M-Y < 0.5, dominated by single dissociation (SD), and 0.5 < log(10)M(Y) < 1.1, dominated by double dissociation (DD), where M-x and M-y are given in GeV. The inclusive pp cross section is also measured as a function of the width of the central pseudorapidity gap Delta eta for Delta eta > 3, logio M-X > 1.1, and logioMy > 1.1, a region dominated by DD. The cross sections integrated over these regions are found to be, respectively, 2.99 0.02(staf)12392(sysf) mb, 1.18 +/- 0.02(stat) +/- 0.13(syst) mh, and 0.58 +/- 0.01(stat)(-0.11)(+0.13) (syst) mh, and are used to extract extrapolated total SD and DD cross sections. In addition, the inclusive differential cross section, d sigma/d Delta eta(F), for events with a pseudorapidity gap adjacent to the edge of the detector, is measured over Delta eta F = 8.4 units of pseudorapidity. The results are compared to those of other experiments and to theoretical predictions and found compatible with slowly 'rising diffractive cross sections as a function of center-of-mass energy.