[Tex/LaTex] Package keyval Error 15 undefined

compilingerrors

When I try to compile the following code on Windows using MikTeX and TexWorks, i get this error : 

! Package keyval Error: 15 undefined.
See the keyval package documentation for explanation.
Type H <return> for immediate help.
...

this is a code source : 

%%%%%%%%%%%%%%%%% Préambule %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass[12pt,a4paper]{report}


\usepackage[hmargin=2cm,vmargin=2cm]{geometry}                  %%%%%%%%%%% marges horizontales et verticales

\usepackage{amsmath,amsthm}
\usepackage{amsfonts}
\usepackage{amssymb,amsmath,latexsym}
\usepackage{graphics}                               
\usepackage[pdftex]{graphicx}                           %%%%%%%%%%%  graphicx pour includegraphics
\usepackage[applemac]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{ae,aecompl}
\usepackage[francais]{babel}                                %%%%%%%%%%% règles de typographie à la française ; francais ou frenchb sont équivalents

%\renewcommand{\bibname}{R\'ef\'erences}



\bibliographystyle{style utilis\'e}
\numberwithin{equation}{subsection}


 \newtheorem{thm}{Th\'{e}or\`{e}me}[section]
 \newtheorem{cor}[thm]{Corollaire}
 \newtheorem{lem}[thm]{Lemme}
 \newtheorem{prop}[thm]{Proposition}
 \newtheorem{prob}{Probl\`{e}me}

 \newtheorem{defn}[thm]{D\'{e}finition}

 \newtheorem{rem}[thm]{Remarque}
 \newtheorem{ex}{Exemple}
 \numberwithin{equation}{section}
 \newtheorem{nt}{Notation}



\begin{document}

%%%%%%%%%%%%%%%%% Page de Titre %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\thispagestyle{empty}
\begin{center}

\vfill

\includegraphics[width=0,15]{logo_fsa.jpg}

\vspace{1cm}

\large{\textbf{UNIVERSIT\'E GALATASARAY\\
FACULT\'E DES ARTS ET DES SCIENCES\\
D\'EPARTEMENT DE MATH\'EMATIQUES}}

\vfill

\Large\textbf{CLASSIFICATION DES ALG\`EBRES DE LIE\\
DE DIMENSION $\leqslant 4$}

\vfill

\large{ Projet de fin d'\'etudes pr\'{e}par\'{e} par }

\textbf{\c Ci\u{g}dem AK}

\vspace{1.5cm}

\centerline{ Sous la direction de }

\centerline{Prof. Susumu TANABE}

\vfill

\emph{{Mai 2012}}

\vfill
\end{center}



\chapter*{Introduction}
\addcontentsline{toc}{chapter}{Introduction}

Une alg\`{e}bre de Lie est un espace vectoriel muni d'un crochet de Lie, nomm\'{e} ainsi en l'honneur du math\'{e}maticien norv\'{e}gien Sophus Lie.




\chapter*{Remerciements}
\addcontentsline{toc}{chapter}{Remerciements}


\tableofcontents

\chapter{Pr\'{e}liminaires}


\chapter{Alg\`{e}bre de Lie}


\section{D\'efinition D'une Alg\`ebre de Lie}

\begin{defn}[crochet de Lie]Soit $V$ un espace vectoriel sur le corps $\mathbb R$. Un \emph{crochet de Lie sur $V$} est une application .... qui v\'erifie ....\end{defn}

.......

\begin{thm}[th\'eor\`eme de Lie] .... \end{thm}

\section{Sous-Alg\`{e}bres et Ideaux}

........


\subsection{Constantes de Structure}

...........

\chapter{Classification des Alg\`{e}bres de Lie en Dimension $\leq 4$}

....................

\section{Alg\`{e}bres de Lie de dimensions 1 sur $\mathbb C$}

..........

\section{Alg\`{e}bres de Lie de dimensions 2 sur $\mathbb C$}

.........

\subsection{Alg\`{e}bre de Lie de dim$L'=1$}

..........


\newpage
\begin{thebibliography}{10}
\addcontentsline{toc}{chapter}{Bibliographie}
  \bibitem{Erdmann2006}
    K. ERDMANN et M. J. WILDON, {\em Introduction to Lie Algebras},
    \newblock (chapitre 1, 2 et 3)
    \newblock Springer-Verlag London Limited, 2006.
\\\\
\textbf{Articles}
  \bibitem{Basili2002}
    R. BASILI,
    \newblock {\em Resolutions of Singularities of Varieties of Lie Algebras of Dimensions 3 and 4},
    \newblock Journal of Lie Theory, Volume 12, pp 397-407, Helderman Verlag, 2002.
\\\\
\textbf{Th\`eses ou M\'emoires}
    \bibitem{Kray2002}
    M. KRAY,
    \newblock {\em Alg\`ebres de Lie, applications aux particules \'el\'ementaires},
    \newblock rapport de Stage de Magist\`ere, Universit\'e Louis Pasteur, Strasbourg, 2008.

  \end{thebibliography}


\end{document}

Best Answer

The error comes from the line

\includegraphics[width=0,15]{logo_fsa.jpg}

The main error is that you have used a comma (,) instead of a period (.). Since the optional argument of \includegraphics is a "key=value" list, 15 is taken as a key which has no meaning.

Moreover, the value of width must be a length, and 0.15 is not a valid one.

So you can either specify something like 0.15\linewidth or a fixed one like 5cm.

Probably you wanted to write

\includegraphics[width=0.15\linewidth]{logo_fsa.jpg}
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