\contentsline {section}{\tocsection {}{}{Introduction}}{1}
\contentsline {section}{\tocsection {}{1}{Approximation for hypersurfaces of low degree}}{2}
\contentsline {section}{\tocsection {}{2}{Ordinary singularities reviewed}}{5}
\contentsline {section}{\tocsection {}{3}{Managing free curves}}{7}
\contentsline {section}{\tocsection {}{4}{Weak approximation at places with ordinary double points}}{9}
\contentsline {section}{\tocsection {}{5}{Applications to cubic hypersurfaces}}{16}
\contentsline {section}{\tocsection {}{}{Appendix: Recent developments for hypersurfaces of low degree}}{17}
\contentsline {section}{\tocsection {}{}{References}}{18}