Analysis of data on low energy piN-->pipiN reaction. I. Total cross sections

This is the first of a series of papers on a consistent model independent analysis of the complete experimental information on the reaction $\pi N \rightarrow \pi \pi N$ at pion momenta up to 500 MeV/c. The paper summarizes the theoretical approach and details of the computational procedure. The complete database on total cross sections in 5 $\pi \pi N$ channels is given together with a critical discussion of their model independent analysis.