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+\documentclass[a4paper]{article}
+% \usepackage{textcomp}
+\usepackage[colorlinks=true,linkcolor=blue]{hyperref}
+\usepackage{bookmark}
+\usepackage{parskip}
+
+\usepackage[tuenc]{fontspec}
+\setmainfont{Linux Libertine O}
+\setsansfont{Linux Biolinum O}
+% \setmainfont{DejaVu Serif}
+% \setmainfont{Droid Serif} % only monotonic Greek (subset of Greek and Coptic)
+
+\usepackage[greek,english]{babel}
+% \languageattribute{greek}{polutoniko}
+\languageattribute{greek}{ancient}
+
+\message{greek-euenc ist}
+\makeatletter
+\@ifl@aded{def}{greek-fontenc}{\message{geladen}}{\message{nicht geladen}}
+\makeatother
+
+
+\begin{document}
+
+\title{Greek support for Babel with XeTeX/LuaTeX}
+\author{Günter Milde}
+\date{2016/09/07}
+\maketitle
+
+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).
+Examples for suitable fonts are the «Deja Vu», «Linux Libertine», or
+«Free Serif» OpenType fonts.
+
+\section{Language Switch}
+
+The declaration \verb|\selectlanguage| switches between languages.
+
+\begin{quote}
+ \selectlanguage{greek}
+ Τί φήις; Ἱδὼν ἐνθέδε παῖδ’ ἐλευθέραν
+ τὰς πλησίον Νύμφας στεφανοῦσαν, Σώστρατε,
+ ἐρῶν άπῆλθες εὐθύς;
+\end{quote}
+
+The command \verb|\foreignlanguage| sets its second argument in the language
+specified as first argument. This is intended for short text parts like
+\foreignlanguage{greek}{Βιβλιοθήκη}.
+
+\section{Font Encoding}
+
+Every language switch to \texttt{greek} calls the \verb|\extrasgreek|
+command which in turn calls \verb|\greekscript| to ensure a Greek-supporting
+font encoding (LGR, TU, EU1, or EU2). Under XeTeX/LuaTeX the font encoding
+normally just remains Unicode (TU, EU1, or EU2). For customization, you can
+add to or redefine the \verb|\extrasgreek| command.
+
+The LGR font encoding does not support Latin characters. Therefore, the
+Babel core defines the declaration \verb|\latintext| and the command
+\verb|\textlatin| to switch to the TU, EU1, EU2, T1 or OT1 font encoding or
+typeset the argument using this encoding. At this point, the «latinencoding»
+is \latinencoding.
+
+Every language switch from \texttt{greek} calls the \verb|\noextrasgreek|
+command which in turn calls \verb|\latintext|.\\
+For customization, you can
+add to or redefine the \verb|\noextrasgreek| command.
+
+With the Unicode font encodings TU, EU1 (XeTeX), or EU2 (LuaTeX),
+Latin characters can be used in Greek text parts and
+input via the «LGR Latin transcription» is not possible.%
+\footnote{%
+ The \emph{xunicode} package provides with the \texttt{tipa} emulation an
+ example how this could be achieved also for Unicode fonts. Alternatively,
+ LGR encoded fonts can be used (see test-unicode-lgr.tex).
+}
+
+\begin{quote}
+ \greekscript Φίλων τοῦ \textlatin{TeX} (ΕΦΤ) --
+ \latintext Friends (\ensuregreek{F\'ilwn}) of TeX.%
+ \footnote{Compare the printout to the similar example in test-greek.pdf.}
+\end{quote}
+
+\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.
+
+If \emph{fontspec} is loaded, \emph{babel-greek} loads Greek LICR
+definitions for the Unicode font encoding (TU, EU1 or EU2) from the file
+\texttt{greek-euenc.def} provided with
+\href{http://www.ctan.org/pkg/greek-fontenc}{greek-fontenc} since
+version~0.10.
+
+With this setup, it is also possible to use accent macros instead of
+pre-composed Unicode characters for letters with diacritics:
+«Τ\'ι φ\'ηις;», «\`<ορα = \accdasiavaria{ο}ρα».
+
+
+\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).
+
+You may redefine the commands \verb+\textdexiakeraia+ and
+\verb+\textaristerikeraia+ to some substitute characters.
+Or, 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}