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This paper presents a detailed description of the CamSpec likelihood whichhas been used to analyse Planck temperature and polarization maps of the cosmicmicrowave background since the first Planck data release. We have created anumber of likelihoods using a range of Galactic sky masks and different methodsof temperature foreground cleaning. Our most powerful likelihood uses 80percent of the sky in temperature and polarization. Our results show that thesix-parameter LCDM cosmology provides an excellent fit to the Planck data.There is no evidence for statistically significant internal tensions in thePlanck TT, TE and EE spectra computed for different frequency combinations. Wepresent evidence that the tendencies for the Planck temperature power spectrato favour a lensing amplitude A_L>1 and positive spatial curvature are causedby statistical fluctuations in the temperature power spectra. Using ourstatistically most powerful likelihood, we find that the A_L parameter differsfrom unity at no more than the 2.2 sigma level. We find no evidence foranomalous shifts in cosmological parameters with multipole range. In fact, weshow that the combined TTTEEE likelihood over the restricted multipole range2-800 gives cosmological parameters for the base LCDM cosmology that are veryclose to those derived from the full multipole range 2-2500. We present revisedconstraints on a few extensions of the base LCDM cosmology, focussing on thesum of neutrino masses, number of relativistic species and the tensor-scalarratio. The results presented here show that the Planck data are remarkablyconsistent between detector-sets, frequencies and sky area. We find no evidencein our analysis that cosmological parameters determined from the CamSpeclikelihood are affected to any significant degree by systematic errors in thePlanck data (abridged).

A Detailed Description of the CamSpec Likelihood Pipeline and a Reanalysis of the Planck High Frequency Maps