We present a rigorous derivation of a real-space full-potential multiple scattering theory(FP-MST) that is free from the drawbacks that up to now have impaired its development(in particular the need to expand cell shape functions in spherical harmonics andrectangular matrices), valid both for continuum and bound states, under conditions forspace partitioning that are not excessively restrictive and easily implemented.In this connection we give a new scheme to generate local basis functions forthe truncated potential cells that is simple, fast, efficient, valid for any shapeof the cell and reduces to the minimum the number of spherical harmonics inthe expansion of the scattering wavefunction. The method also avoids the needfor saturating ‘internal sums’ due to the re-expansion of the spherical Hankelfunctions around another point in space (usually another cell center). Thus thisapproach provides a straightforward extension of MST in the muffin-tin (MT)approximation, with only one truncation parameter given by the classical relationlmax = kRb, wherek isthe electron wavevector (either in the excited or ground state of the system under consideration) andRb is the radius of the bounding sphere of the scattering cell. Moreover, the scattering pathoperator of the theory can be found in terms of an absolutely convergent procedure in the limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viablemethod for electronic structure calculations and makes possible the computation of x-rayspectroscopies, notably photo-electron diffraction, absorption and anomalous scatteringamong others, with the ease and versatility of the corresponding MT theory. Somenumerical applications of the theory are presented, both for continuum and bound states.