\contentsline {section}{\tocsection {}{}{Introduction}}{1}
\contentsline {subsection}{\tocsubsection {}{0.1}{Gromov--Witten theory and relative stable maps}}{1}
\contentsline {section}{\tocsection {}{1}{Basic examples}}{2}
\contentsline {subsection}{\tocsubsection {}{1.1}{Plane sections of a quadric surface}}{2}
\contentsline {subsection}{\tocsubsection {}{1.2}{Rational curves of type $(2,2)$}}{2}
\contentsline {subsection}{\tocsubsection {}{1.3}{Plane section of a cubic}}{3}
\contentsline {section}{\tocsection {}{2}{The degeneration scheme: old picture}}{5}
\contentsline {section}{\tocsection {}{3}{The case of a normal crossings divisor}}{7}
\contentsline {subsection}{\tocsubsection {}{3.1}{Comparing old and new: a normal crossings divisor has already appeared}}{8}
\contentsline {subsection}{\tocsubsection {}{3.2}{Old picture: the expansions are normal crossings varieties}}{8}
\contentsline {subsection}{\tocsubsection {}{3.3}{Old picture: curves meet the strata properly}}{9}
\contentsline {subsection}{\tocsubsection {}{3.4}{Old picture: relative stable maps can be glued}}{11}
\contentsline {subsection}{\tocsubsection {}{3.5}{Old picture: we can glue two curves to get any degenerate picture}}{15}
\contentsline {subsection}{\tocsubsection {}{3.6}{Old picture: the horrors of deformation theory}}{16}
\contentsline {section}{\tocsection {}{}{References}}{16}