\documentclass{book}

\begin{document}

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\frontmatter

\chapter{Preface}
Preface.

\section{Acknowledgements}

\chapter[Other]{Other frontmatter chapter}

\tableofcontents

\mainmatter

\chapter*{Test chapter 1}
Test of starred chapter.

\chapter{Test chapter 1}
This test document is created to test advanced TOC functionality.

\section{Test section 1}

\subsection{sub}

\subsubsection{subsub}

\subsubsubsection{subsub}

\subsection{Test sub section 1}

\section{$\alpha$}

\subsection{Test sub section 1}

\subsection{Test sub section 2}
Some text.

\chapter{Test chapter 2}

\section{Testing TOC levels}
Testing more input and TOC levels.

\subsection{Testing TOC sub levels}

\subsubsection{Testing TOC sub sub levels}
Hello world.

\subsubsection{Text $\Gamma^{r}(\ensuremath{{\mathbf{Z}}}_p^d,\mathbf{K})$}

\subsection{Another test subsection}

\subsubsection{Other text $\Gamma^{r}$}

\section{Testing more appendix levels}
Testing more input and TOC levels.

\subsection{Testing TOC sub levels}

\appendix

\chapter{Appendix 1}
This test document is created to test advanced TOC functionality.

\section{Appendix subsection}

\subsection{sub}

\subsubsection{subsub}

\subsubsubsection{subsub}

\subsection{Test sub section 1}

\chapter{Appendix 2}

\section{Testing TOC levels}
Testing more input and TOC levels.

\subsection{Testing TOC sub levels}

\subsubsection{Testing TOC sub sub levels}
Hello world.

\subsubsection{Text $\Gamma^{r}(\ensuremath{{\mathbf{Z}}}_p^d,\mathbf{K})$}

\subsection{Another test subsection}

\subsubsection{Other text $\Gamma^{r}$}

\section{Testing more appendix levels}
Testing more input and TOC levels.

\subsection{Testing TOC sub levels}


\backmatter

\chapter{No numbers in backmatter 1}

\section{Section 1}

\section{Section 2}

\chapter{No numbers in backmatter 2}

\section{Section 1}

\section{Section 2}

\end{document}