Measurements of cross sections of inelastic and diffractive processes in proton-proton collisions at LHC energies were carried out with the ALICE detector. The fractions of diffractive processes in inelastic collisions were determined from a study of gaps in charged particle pseudorapidity distributions: for single diffraction (diffractive mass MX <200 GeV/c2) [Formula: see text], and [Formula: see text], respectively at centre-of-mass energies [Formula: see text]; for double diffraction (for a pseudorapidity gap Δη>3) σDD/σINEL=0.11±0.03,0.12±0.05, and [Formula: see text], respectively at [Formula: see text]. To measure the inelastic cross section, beam properties were determined with van der Meer scans, and, using a simulation of diffraction adjusted to data, the following values were obtained: [Formula: see text] mb at [Formula: see text] and [Formula: see text] at [Formula: see text]. The single- and double-diffractive cross sections were calculated combining relative rates of diffraction with inelastic cross sections. The results are compared to previous measurements at proton-antiproton and proton-proton colliders at lower energies, to measurements by other experiments at the LHC, and to theoretical models.