Between section 32 and Appendix A (On Page 68), I manually added unnumbered sections called "Summary" "Further Reading" and "Acknowledgment" by typing

\begin{center}
{\Large\bf Summary}
\end{center}

\begin{center}
\end{center}

\begin{center}
{\Large\bf Acknowledgment}
\end{center}


However, I also want to add these unnumbered sections to the Table of Contents between Section 32 and Appendix A. I am afraid if I type \section*{Summary}instead of \begin{center}{\Large\bf Summary}\end{center} the word "Summary" would not appear in the middle of the line. Nor does it seem that \section*{Summary} would make the Section "Summary" appear in the Table of Contents. What should I do?

Like this?

\documentclass{article}
\usepackage{lipsum}
\begin{document}
\tableofcontents
\section{Whatever}
\lipsum[1-5]
\section*{Summary}
\lipsum[6-10]
\end{document}


Don't use \begin{center} {\Large\bf Acknowledgment} \end{center} and \bf!!! I recommend something like this:

\documentclass{article}
\usepackage{lipsum}
\usepackage{titlesec}
\titleformat{\section}{\Large\bfseries}{\thesection}{2ex}{\centering}
\begin{document}
\tableofcontents
\section{Whatever}
\lipsum[1-5]
\section*{Summary}
\lipsum[6-10]
\end{document}


In case you don't want to center numbered sections, I recommend defining a macro. However, this way lacks consistency, so it is not good.

\documentclass{article}
\usepackage{lipsum}
\newcommand\yoursection[1]{%
\begin{center}
\Large\bfseries#1
\end{center}
}
\begin{document}
\tableofcontents
\section{Whatever}
\lipsum[1-5]
\yoursection{Summary}
\lipsum[6-10]
\end{document}


You may also use the excellent KOMA-script bundle, and utilise the addsec-command, which gives you an unnumbered section, which behaves like all other sections. (You have similar commands for other sectioning commands addpart, addchap).

\documentclass{scrartcl}
\usepackage{lipsum}
\begin{document}
\tableofcontents
\section{Whatever}
\lipsum[1-5]