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Total cross sections have been measured for electron capture and stripping of ${\mathrm{He}}^{+}$, ${\mathrm{Ne}}^{+}$, and ${\mathrm{A}}^{+}$ ions in single collisions of ${\mathrm{He}}^{+}$ on He, Ne, and A; ${\mathrm{Ne}}^{+}$ on Ne and A; and ${\mathrm{A}}^{+}$ on A. Where ${\mathrm{He}}^{+}$ ions are incident, the cross sections are given for electron capture, ${\ensuremath{\sigma}}_{10}$; for electron loss, ${\ensuremath{\sigma}}_{12}$; and for "elastic" scattering in excess of one degree, ${\ensuremath{\sigma}}_{11}g1\ifmmode^\circ\else\textdegree\fi{}$. Where ${\mathrm{Ne}}^{+}$ and ${\mathrm{A}}^{+}$ are incident, the cross sections for multiple stripping ${\ensuremath{\sigma}}_{13}, \ensuremath{\cdots}, {\ensuremath{\sigma}}_{17}$ are given also. The measurements were made at 25, 50, and 100 kev and at additional energies in two cases where a maximum in the electron capture cross section was observed. Each total cross section was compiled by adding the contributions from the various angular regions into which the incident particle may be scattered. The contribution from the particles scattered between 0\ifmmode^\circ\else\textdegree\fi{} and 1\ifmmode^\circ\else\textdegree\fi{} was measured directly, while that for regions in excess of 1\ifmmode^\circ\else\textdegree\fi{} was obtained by integrating the measured differential cross sections. In the region between 1\ifmmode^\circ\else\textdegree\fi{} and 4\ifmmode^\circ\else\textdegree\fi{} the differential cross section for each process was measured with high resolution and these data are presented here separately. These differential measurements supplement data previously published for angles in excess of 4\ifmmode^\circ\else\textdegree\fi{}. Tables are presented showing the contribution of each of the angular regions to the various total cross sections. Large-angle scattering is found to make a significant contribution to the total cross sections for the production of the more highly ionized particles.