Insert Table of Contents in chapter

Here is a quick (stock) answer for this:

The easiest way is to use etoc package and its localtableofcontents macro, at the appropriate place. The manual is at https://ctan.org/pkg/etoc.

documentclass{book}

usepackage{etoc}


begin{document}
tableofcontents % Global toc
chapter{First}
localtableofcontents % local toc
section{First section}

chapter{Second}
localtableofcontents

section{First section of 2nd chapter}

end{document}

Edit Here is the memoir version.

For some reasons I can't figure out (the manual of etoc is not really clear in this case) it's necessary to use localtableofcontents*. The individual tocdepth can be controlled with the etocsettocdepth.toc{sectionlevel} command (note the .toc in the macro name`)

documentclass{memoir}

usepackage{blindtext}
usepackage{etoc}


setsecnumdepth{subsection}
etocsettocdepth{subsection}
begin{document}

tableofcontents % Global toc
chapter{First}
etocsettocdepth.toc{section}

localtableofcontents*
section{First section}
subsection{First subsection -- not in the local toc}

blindtext

chapter{Second}
etocsettocdepth.toc{subsection}
localtableofcontents*

section{First section of 2nd chapter}
subsection{First subsection of first section of 2nd chapter}

end{document}