"Inspirational" quote at start of chapter

I think it is the package epigraph and is included in both TeX Live and MiKTeX distributions.

\documentclass{book}
\usepackage{epigraph}
\begin{document}
\chapter{First Chapter}
\epigraph{I recall seeing a package to make quotes}{Snowball}
\end{document}

The memoir document class offers "out of the box" commands \chapterprecis, \chapterprecishere, and \chapterprecistoc:

\documentclass{memoir}

\begin{document}

\chapter{Graph Theory}
\chapterprecishere{``Begin at the beginning,¨ the King said gravely, ``and
go on till you come to the end: then stop."\par\raggedleft--- \textup{Lewis
Carroll}, Alice in Wonderland}

\end{document}

As Brent.Longborough mentions in his comment, memoir also offers an \epigraph command and an epigraph environment:

\documentclass{memoir}

\epigraphfontsize{\small\itshape}
\setlength\epigraphwidth{8cm}
\setlength\epigraphrule{0pt}

\begin{document}

\chapter{Graph Theory}

\epigraphfontsize{\small\itshape}
\epigraph{``Begin at the beginning," the King said gravely, ``and go on till you
come to the end: then stop."}{--- \textup{Lewis Carroll}, Alice in Wonderland}


\end{document}

You can also do it yourself:

\documentclass{book}

\makeatletter
\renewcommand{\@chapapp}{}% Not necessary...
\newenvironment{chapquote}[2][2em]
  {\setlength{\@tempdima}{#1}%
   \def\chapquote@author{#2}%
   \parshape 1 \@tempdima \dimexpr\textwidth-2\@tempdima\relax%
   \itshape}
  {\par\normalfont\hfill--\ \chapquote@author\hspace*{\@tempdima}\par\bigskip}
\makeatother

\begin{document}
\chapter{Graph Theory}

\begin{chapquote}{Lewis Carroll, \textit{Alice in Wonderland}}
``Begin at the beginning,'' the King said, gravely, ``and go on till you
come to an end; then stop.''
\end{chapquote}

\noindent The Pregolya River passes through the city once known as K\"onigsberg. In the 1700s
seven bridges were situated across this river in a manner similar to what you see
in Figure \ldots
\end{document}

The above MWE provides the chapquote environment that takes one argument - the author of the quote. It indents the quote by 2em (default), but that can also be changed via an optional argument:

\begin{chapquote}[30pt]{author}
  %... your quote
\end{chapquote}

The default setting is in \itshape, with a right-aligned "author".