This is the first of a series of papers on a consistent model-independ
ent analysis of the complete experimental information on the reaction
pi N --> 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.