\documentclass[a4paper]{article}
% \usepackage{textcomp}
\usepackage{hyperref,bookmark}
\usepackage{parskip}

% Declare the font encoding and Greek LICR definitions:
\usepackage[LGR]{fontenc}
\usepackage{textalpha}[2013/09/11]

% Set up Latin Modern OpenType unicode font
\usepackage{fontspec}

\usepackage[greek,english]{babel}
% \languageattribute{greek}{polutoniko}

% use LGR (8-bit CB-fonts) instead of Unicode fonts for Greek:
% \renewcommand*{\greekscript}{\fontencoding{LGR}\selectfont}
\addto{\extrasgreek}{\greektext}


\begin{document}


\section*{XeTeX/LuaTeX with LGR fonts}

The babel option «greek» activates the support for the Greek language
defined in the file «greek.ldf» (source «greek.dtx»).

Typesetting Greek texts requires a font containing Greek letters. With the
XeTeX or LuaTeX engines, the user must ensure that the selected font
contains the required glyphs (the default Latin Modern fonts miss them).

Latin Modern can combined with the matching CB-Greek 8-bit font. For the
setup, see the preamble of this document \texttt{test-unicode-lgr.tex}

Caveat: Currently, hyphenation does not work with this setup. Use it only
for short Greek quotes or as a last ressort.

\section{Language Switch}

The declaration \verb|\selectlanguage| switches between languages.
With XeTeX/LuaTeX and LGR, Unicode input is not possible. Instead, use the
Latin transliteration or LICR macros:

\begin{quote}
  \selectlanguage{greek}
  T'i f'hic? <Id`wn >enj'ede pa~id'' >eleuj'eran\\
  t`ac plhs'ion N'umfac stefano~usan, S'wstrate,\\
  >er~wn 'ap~hljec e>uj'uc?
\end{quote}

The macro \verb|\foreignlanguage| sets its second argument in the specified
language. This is intended for short text parts like
\foreignlanguage{greek}{Βιβλιοθήκη}.

\section{Font Encoding}

Switching to a font encoding supporting the Greek script is possible without
switching the Babel language using the declarations \verb|\greekscript| or
\verb|\greektext| (always LGR) and the macros \verb|\ensuregreek| or
\verb|\textgreek|. These commands do not start a new paragraph.

The Babel core defines the declaration \verb|\latintext| and the command
\verb|\textlatin| to switch to the T1 or OT1 font encoding or typeset the
argument using this encoding. greek-fontenc adds a test for EU1 and EU2, if
the TeX engine is XeTeX or LuaTeX. Here, the «latinencoding» is
\latinencoding.

With XeTeX or LuaTeX, the macros \verb|\greektext| and \verb|\textgreek| 
are only defined, if the LGR font encoding is loaded via the
\texttt{fontenc} package (see test-unicode-lgr.tex).

% don't change the font encoding.
With LGR, Latin characters in Greek text parts are typeset as Greek characters
according to the Latin transcription defined in LGR.%

\begin{quote}
  \greektext F\'ilwn to\~u \textlatin{TeX} (EFT) --
  \latintext{Friends (\textgreek{F\'ilwn}) of TeX.}%
\end{quote}

\section{MakeUppercase, MakeLowercase}

Capital Greek letters have diacritics (except the dialytika and sub-iota) to
the left (instead of above) and drop them in uppercase.

Tonos and dasia mark a \emph{hiatus} (break-up of a diphthong) if placed on
the first vowel of a diphtong (\textgreek{\'ai, \'au, \'ei, \'>ai, \'>au,
\'>ei}). A dialytika must be placed on the second vowel if they are dropped.
(\foreignlanguage{greek}{\MakeUppercase{\'ai, \'au, \'ei, \'>ai, \'>au,
\'>ei}}).

\section{LICR Macros}

Babel defines macros for several autogenerated strings so that they may
appear in the choosen language. \emph{babel-greek} uses LICR macros in
order to let the string macros work independent of the font encoding.

Until automatically done by \emph{euenc} for EU1 and EU2 font encodings, the
recommended way to load Greek LICR definitions is via the \emph{textalpha}
or \emph{alphabeta} packages provided with \emph{greek-fontenc} since
version~0.10.

\subsection{Hiatus}

The «hiatus» feature works with macro input:

\selectlanguage{greek}
% from teubner: άυλος/ΑΫΛΟΣ
\acctonos\textalpha\textupsilon λος $\mapsto$
\MakeUppercase{\acctonos\textalpha\textupsilon λος},
\>'\textalpha\textupsilon λος $\mapsto$
\MakeUppercase{\>'\textalpha\textupsilon λος},
% from http://diacritics.typo.cz/index.php?id=69  μάινα -> ΜΑΪΝΑ
m\acctonos\textalpha\textiota να $\mapsto$
\MakeUppercase{m\acctonos\textalpha\textiota να},
% from  http://de.wikipedia.org/wiki/Neugriechische_Orthographie#Das_Trema
% κέικ, ἀυπνία/αϋπνία
\textkappa\acctonos\textepsilon\textiota\textkappa $\mapsto$
\MakeUppercase{\textkappa\acctonos\textepsilon\textiota\textkappa},
\>\textalpha\textupsilon πνία $\mapsto$
\MakeUppercase{\>\textalpha\textupsilon πνία}.
\selectlanguage{english}

\subsection{Captions}

\selectlanguage{greek}
\prefacename,
\refname,
\abstractname,
\bibname,
\chaptername,
\appendixname,
\contentsname,
\listfigurename ,
\listtablename,
\indexname,
\figurename,
\tablename,
\partname,
\enclname,
\ccname,
\headtoname,
\pagename,
\seename,
\alsoname,
\proofname,
\glossaryname
\selectlanguage{english}

Test correct upcasing (dropping of accents):

\selectlanguage{greek}
\MakeUppercase{
\prefacename,
\refname,
\abstractname,
\bibname,
\chaptername,
\appendixname,
\contentsname,
\listfigurename,
\listtablename,
\indexname,
\figurename,
\tablename,
\partname,
\enclname,
\ccname,
\headtoname,
\pagename,
\seename,
\alsoname,
\proofname,
\glossaryname
}
\selectlanguage{english}


\subsection{Months}

\selectlanguage{greek}
\newcounter{foo}
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\stepcounter{foo} \month=\value{foo} \today \\
\selectlanguage{english}

\section{Greek Numerals}

See greek.pdf for the formation rules of Greek numerals.
Some examples:

\selectlanguage{greek}

\greeknumeral{1},
\greeknumeral{2},
\greeknumeral{3},
\greeknumeral{4},
\greeknumeral{5},
\greeknumeral{6},
\greeknumeral{7},
\greeknumeral{8},
\greeknumeral{9},
\greeknumeral{10},
\greeknumeral{11},
\greeknumeral{12},
\greeknumeral{20},
\greeknumeral{345},
\greeknumeral{500},
\greeknumeral{1997},
\greeknumeral{2013},

\Greeknumeral{1},
\Greeknumeral{2},
\Greeknumeral{3},
\Greeknumeral{4},
\Greeknumeral{5},
\Greeknumeral{6},
\Greeknumeral{7},
\Greeknumeral{8},
\Greeknumeral{9},
\Greeknumeral{10},
\Greeknumeral{11},
\Greeknumeral{12},
\Greeknumeral{20},
\Greeknumeral{345},
\Greeknumeral{500},
\Greeknumeral{1997},
\Greeknumeral{2013},


Enumerated lists use Greek characters/numerals in the second and fourth level:

\selectlanguage{greek}
\begin{enumerate}
  \item item 1
  \begin{enumerate}
    \item item 1.1
    \begin{enumerate}
      \item item 1.1.1
       \begin{enumerate}
         \item item 1.1.1.1
         \item item 1.1.1.2
       \end{enumerate}
      \item item 1.1.2
    \end{enumerate}
  \end{enumerate}
\end{enumerate}
\selectlanguage{english}


This may be problematic with fonts that only partially support Greek and
miss the numeral signs (dexiakeraia and aristerikeraia). If you prefer the
"normal" enumeration, write in the preamble after loading babel:

\begin{verbatim}
  \makeatletter
  \addto\extrasgreek{\let\@alph\latin@alph
  		     \let\@Alph\latin@Alph}
  \makeatother
\end{verbatim}

\end{document}
