Measurements of diffractive dissociation cross sections in pp collisions at √s=7 TeV are presented in kinematic regions defined by the masses MX and MY 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 ξX=M2X/s in the region −5.5<log10ξX<−2.5, for log10MY<0.5, dominated by single dissociation (SD), and 0.5<log10MY<1.1, dominated by double dissociation (DD), where MX and MY are given in GeV. The inclusive pp cross section is also measured as a function of the width of the central pseudorapidity gap Δη for Δη>3, log10MX>1.1, and log10MY>1.1, a region dominated by DD. The cross sections integrated over these regions are found to be, respectively, 2.99±0.02(stat)+0.32−0.29(syst) mb, 1.18±0.02(stat)±0.13(syst) mb, and 0.58±0.01(stat)+0.13−0.11(syst) mb, and are used to extract extrapolated total SD and DD cross sections. In addition, the inclusive differential cross section, dσ/dΔηF, for events with a pseudorapidity gap adjacent to the edge of the detector, is measured over ΔηF=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.11 MoreReceived 30 March 2015DOI:https://doi.org/10.1103/PhysRevD.92.012003This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.© 2015 CERN, for the CMS Collaboration