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This is my code:

%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode

\documentclass[a4paper]{article}
\usepackage{fontspec}
\usepackage{xunicode}
\usepackage{xltxtra}
\setmainfont[Mapping=tex-text]{Brill-Roman}
\begin{document}
This is a text.
\textit{Here goes!}
\end{document}

I have updated the admin package manager successfully, but it still doesn't work:

This is XeTeX, Version 3.1415926-2.4-0.9998 (MiKTeX 2.9)
entering extended mode
("C:\Users\Guillaume\Desktop\Medlye\Brill roman essai.tex"
LaTeX2e 
Babel  and hyphenation patterns for english, afrikaans, ancientgreek, ar
abic, armenian, assamese, basque, bengali, bokmal, bulgarian, catalan, coptic, 
croatian, czech, danish, dutch, esperanto, estonian, farsi, finnish, french, ga
lician, german, german-x-2012-05-30, greek, gujarati, hindi, hungarian, iceland
ic, indonesian, interlingua, irish, italian, kannada, kurmanji, latin, latvian,
 lithuanian, malayalam, marathi, mongolian, mongolianlmc, monogreek, ngerman, n
german-x-2012-05-30, nynorsk, oriya, panjabi, pinyin, polish, portuguese, roman
ian, russian, sanskrit, serbian, slovak, slovenian, spanish, swedish, swissgerm
an, tamil, telugu, turkish, turkmen, ukenglish, ukrainian, uppersorbian, usengl
ishmax, welsh, loaded.
("C:\Program Files\MiKTeX 2.9\tex\latex\base\article.cls"
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
("C:\Program Files\MiKTeX 2.9\tex\latex\base\size10.clo"))
("C:\Program Files\MiKTeX 2.9\tex\latex\fontspec\fontspec.sty"
(C:\Users\Guillaume\AppData\Roaming\MiKTeX\2.9\tex\latex\l3kernel\expl3.sty
("C:\Program Files\MiKTeX 2.9\tex\xelatex\xgreek\expl3\l3names.sty")

LaTeX Warning: You have requested, on input line 48, version
               `2011/12/30' of package l3names,
               but only version
               `1998/04/20 v2.0b L3 Experimental Naming Scheme for TeX Primitiv
es'
               is available.


! Package expl3 Error: MismatchedLaTeX3packagesdetected..

See the expl3 package documentation for explanation.
Type  H   for immediate help.
 ...                                              

l.59   }
    
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closed as too localized by Marco Daniel, percusse, Joseph Wright Jun 18 '12 at 6:54

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You have mismatched versions of fontspec and expl3. As you use MiKTeX, use the package manger to make sure that l3kernel and l3packages are installed, and remove expl3 and xpackages if they are installed. –  Joseph Wright Jun 13 '12 at 21:49
    
See also tex.stackexchange.com/questions/23254/… –  Joseph Wright Jun 13 '12 at 21:52
1  
In the past, the LaTeX3 code was packaged in MiKTeX as expl3 and xpackages. We altered this some time ago to l3kernel and l3packages, but sometimes you have to remove the older versions by hand. –  Joseph Wright Jun 14 '12 at 8:15
1  
First run the package manager as Admin, and remove (if present) expl3 and xpackages. Then run the package manager without Admin and do the same. –  Joseph Wright Jun 14 '12 at 8:34
3  
@Guillaume: Your miktex version, your windows version, if you used the package manager in admin or user mode, where you looked for the update manager, which repository you normally use, the exact wording of an error are all things that matter. Don't let us drag every information piecewise out of you. –  Ulrike Fischer Jun 14 '12 at 11:57

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