The paper presents a fast Markov Chain Monte-Carlo (MCMC) exploration of cosmological parameter space, combining results from recent cosmic microwave background (CMB) experiments and other data sources. The authors perform a joint analysis to provide constraints on parameters such as $\sigma_8$ from the CMB alone, and then combine these with data from the Hubble Space Telescope Key Project, 2dF galaxy redshift survey, supernovae Ia, and big-bang nucleosynthesis. The MCMC method allows for the rapid investigation of a large number of parameters, with results presented from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Key findings include constraints on neutrino mass ($m_\nu \lesssim 0.3$ eV), the equation of state of dark energy, and the tensor amplitude. The paper also discusses the impact of additional parameters on the base parameter constraints and the use of importance sampling for various purposes, including computing results from new data and accuracy correction. The authors conclude that simple inflationary models with small tilt and tensor amplitude account for the data well, and there is no evidence for massive neutrinos, a non-zero equation of state for dark energy, or tensor modes using current data.The paper presents a fast Markov Chain Monte-Carlo (MCMC) exploration of cosmological parameter space, combining results from recent cosmic microwave background (CMB) experiments and other data sources. The authors perform a joint analysis to provide constraints on parameters such as $\sigma_8$ from the CMB alone, and then combine these with data from the Hubble Space Telescope Key Project, 2dF galaxy redshift survey, supernovae Ia, and big-bang nucleosynthesis. The MCMC method allows for the rapid investigation of a large number of parameters, with results presented from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Key findings include constraints on neutrino mass ($m_\nu \lesssim 0.3$ eV), the equation of state of dark energy, and the tensor amplitude. The paper also discusses the impact of additional parameters on the base parameter constraints and the use of importance sampling for various purposes, including computing results from new data and accuracy correction. The authors conclude that simple inflationary models with small tilt and tensor amplitude account for the data well, and there is no evidence for massive neutrinos, a non-zero equation of state for dark energy, or tensor modes using current data.