Compilation and R-matrix analysis of Big Bang nuclear reaction rates

40 pages, accepted for publication at ADNDT, web site at http://pntpm3.ulb.ac.be/bigbangWe use the R-matrix theory to fit low-energy data on nuclear reactions involved in Big Bang nucleosynthesis. A special attention is paid to the rate uncertainties which are evaluated on statistical grounds. We provide S factors and reaction rates in tabular and graphical formats