\documentclass{article}
\usepackage[american,greek]{babel}
\languageattribute{greek}{polutoniko}
\usepackage{cmap}
\usepackage{ucs}
\usepackage[utf8x]{inputenc}
\usepackage{athnum,grmath}
\newcommand{\sg}{\selectlanguage{greek}}
\newcommand{\sa}{\selectlanguage{american}}
\begin{document}
\selectlanguage{american}
\title{Writing Greek with the \ttfamily greek\rmfamily\  option of the
\ttfamily babel\rmfamily\ package}
\author{Apostolos Syropoulos\\
        366, 28th October Str.\\
        GR-671 00 Xanthi, GREECE\\
        e-mail: \texttt{asyropoulos@yahoo.com}}
\date{April 8, 1999\\
      July 23, 2009}
\maketitle
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Overview}
The \texttt{greek} option of the \texttt{babel} package is an attempt to
make it possible for someone to write Greek text with \LaTeX. The current
version of the \texttt{greek} option supports the \sg polutonik'o \sa\ 
accentual system of the Greek language. 
Moreover, there is support for Greek numerals. One can produce easily 
valid Greek numerals both in uppercase and lowercase forms, e.g,
\textgreek{\greeknumeral{1997}}\ and \textgreek{\Greeknumeral{1997}}. The
labels in second and fourth level enumerations are lowercase
and uppercase Greek numerals correspondingly. The latest version of
the file (1.2b as of this writing) supports the \verb|polutoniko|
language attribute for people willing to typeset documents in \textgreek{πο\-λυ\-το\-νι\-κό} 
greek.  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Typing Greek Text}
\TeX\ has been designd to understand only 8-bit characters, nevertheless, \LaTeX\
is now able to process UTF-8 encoded files. Therefore, there are several ways to
enter Greek text. First of all, one can prepare a UTF-8 input file, but she must
include the following command in her document's preamble:
\begin{center}
\begin{tabular}{l}
\verb|\usepackage{cmap} %When using pdfLaTeX|\\
\verb|\usepackage{ucs}|\\
\verb|\usepackage[utf8x]{inputenc}|
\end{tabular}
\end{center} 
However, if, for some reason, it is not possible to prepare UTF-8 encoded input files, there is always
the possibility to use the following transliteration:
\begin{center}
\begin{tabular}{|lllllllllllll|}\hline
\textgreek{a}&  
\textgreek{b}&   
\textgreek{g}&  
\textgreek{d}&  
\textgreek{e}&  
\textgreek{z}&  
\textgreek{h}&  
\textgreek{j}&   
\textgreek{i}&   
\textgreek{k}&   
\textgreek{l}&   
\textgreek{m}&
\textgreek{n}\\
a& b& g& d&  e&  z&  h&  j&  i&  k&  l&  m&  n\\
\hline    
\textgreek{x}&  
\textgreek{o}&  
\textgreek{p}&  
\textgreek{r}&  
\textgreek{sv}&  
\textgreek{t}&  
\textgreek{u}&  
\textgreek{f}&  
\textgreek{q}&  
\textgreek{y}&  
\textgreek{w}& 
\textgreek{c}& \hbox{ } \\
x&  o&  p&  r&  s&   
t&  u&  f&  q&  y&  w& c& \hbox{ }\\ \hline
\end{tabular}
\end{center}
In order to produce in isolation the letter \textgreek{sv}, 
on has to type \texttt{sv}. This feature is due to the strong ligature mechanism
that \TeX\ employs.  In the ``modern'' \textgreek{μονοτονικό} accentual system 
only one accent is used---\textgreek{οξεία} (acute). In the traditional \textgreek{πολυτονικό} 
accentual system we 
need more accents and breathing signs. Since the later has some peculiarities,
as far it regards \TeX, we decided to make the primary language the
\textgreek{monotonik'o} and to provide the \textgreek{polutonik'o} as
a dialect. Consequently, if someone wishes to correctly typeset 
\textgreek{polutonik'o}, he must in addition use the \verb|polutoniko| language attribute,

We can produce an accented letter by
prefixing the letter with he symbol that denotes the accent, e.g.,
\texttt{>a'erac} produces the word \sg >a'erac.\sa\footnote{For the 
technically inclined reader, we must say that \TeX\ uses the ligature table of
the font in order to determine the character that corresponds to the
input character sequence.} Here are the symbols that are recognized: 
\begin{center}
\begin{tabular}{cccc}\hline
Accent & Symbol & Example & Output\\ \hline
acute  & \texttt{'} & \texttt{g'ata} & \textgreek{g'ata}\\
grave  & \texttt{`} & \texttt{dad`i} & \textgreek{dad`i}\\
circumflex & \verb+~+ & \verb+ful~hc+ & \sg\textgreek{ful~hc}\sa\\
rough breathing & \verb+<+ & \verb+<'otan+ & \sg\textgreek{<'otan}\sa\\
smooth breathing & \verb+>+ & \verb+>'aneu+ & \sg\textgreek{>'aneu}\sa\\
subscript & \texttt{|} & \verb+>anate'ilh|+ & \sg\textgreek{>anate'ilh|}\\
diaeresis & \texttt{"}& \texttt{qa"ide'uh|c} & \sg\textgreek{qa"ide'uh|c}\\ 
\hline
\end{tabular}
\end{center}
Note that the subscript symbol is placed \textbf{after} the letter.
The last thing someone must know in order to be able to write normal Greek
text is the punctuation marks used in the language:
\begin{center}
\begin{tabular}{ccc}\hline
Punctuation Sign & Symbol & Output\\ \hline
period   & \texttt{.} & \sg\textgreek{.}\sa\\
semicolon & \texttt{;} & \sg\textgreek{;}\sa\\
exclamation mark & \texttt{!} & \sg\textgreek{!}\sa\\
comma & \texttt{,} & \sg\textgreek{,}\sa\\
colon & \texttt{:} & \sg\textgreek{:}\sa\\
question mark & \texttt{?} & \sg\textgreek{?}\sa\\
left apostrophe & \texttt{``} & \sg\textgreek{``}\sa\\
right apostrophe & \texttt{''} & \sg\textgreek{''}\sa\\
left quotation mark & \texttt{((} & \sg\textgreek{))}\sa\\
right quotation mark & \texttt{))} & \sg\textgreek{))}\sa\\ \hline
\end{tabular}
\end{center}
Using these conventions it is a straightforward exercise to write Greek
\textgreek{polutonik'o} text. For example the following excerpt from 
\textgreek{D'uskoloc} of \textgreek{M'enandroc}
\sg
\begin{quote}
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}
\sa can be produced by the following \LaTeX\ code:
\begin{center}
\begin{tabular}{l}
\verb+T'i f'hic? <Id`wn >enj'ede pa~id'' >eleuj'eran+\footnotemark\\
\verb+t`ac plhs'ion N'umfac stefano~usan, S'wstrate,+\\
\verb+>er~wn 'ap~hljec e>uj'uc?+
\end{tabular}
\end{center}
\footnotetext{Please, bear in mind that this work correctly only if we
use the \texttt{polutoniko} language attribute.}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Producing Greek Text}
Once the Greek language is selected with the command 
\begin{center}
\verb+\selectlanguage{greek}+ 
\end{center}
for \textgreek{μονοτικό} or the command
\begin{center}
\begin{tabular}{l}
\verb+\selectlanguage{greek}+\\
\verb=\languageattribute{greek}{polutoniko}=
\end{tabular}
\end{center}
for \textgreek{πολυτονικό}, whatever we type will be typeset with the Greek fonts. 
The command
\verb+\textlatin+ can be used for short passages in some language that
uses the Latin alphabet, while the the command \verb+\latintext+ changes
the base fonts to the ones used by languages that use the Latin alphabet.
However, all words will be hyphenated by following the Greek hyphenation
rules! Similar commands are available once someone has selected some
other language. The commands \verb+\textgreek+ and \verb+\greektext+
behave exactly like their ``Latin'' counterparts. For example, the
word \textgreek{M'imhc} has been produced with the command 
\texttt{\char`\\textgreek\char`\{\textgreek{Μίμης}\char`\}}. Please note that 
certain symbols cannot have
their expected result for Greek text, unless someone has selected the Greek 
language, e.g., \verb+~+ is such a symbol.

As we have mentioned above this version of the \texttt{greek} option of the
\texttt{babel} package supports the use of Greek numerals. The commands
\verb+\greeknumeral+ and \verb+\Greeknumeral+ produce the lowercase and 
the uppercase Greek numeral, e.g., 
\begin{center}
\begin{tabular}{cc}\hline
Command & Output\\ \hline
\verb+\Greeknumeral{9999}+ & \sg\textgreek{\Greeknumeral{9999}}\\
\verb+\greeknumeral{9999}+ & \sg\textgreek{\greeknumeral{9999}}\\
\hline
\end{tabular}
\end{center}
These macros can accept as argument only Arabic numerals. In case
someone wishes to produce the Greek numeral corresponding to the
value of a counter variable, he can use the command \verb|\alph{counter}|.
Moreover, it is now possible to have Greek page numbering by using the
command \verb|\pagenumbering{alph}|. (\verb|\alph| is now a synonym for
\verb|\greeknumeral|, and \verb|\Alph| for \verb|\Greeknumeral|.)
In order to correctly typeset the greek numerals the greek option file
provides the following commands:
\begin{center}
\begin{tabular}{cc}\hline
Command & Output\\ \hline
\verb+\qoppa+ & \textgreek{\qoppa}\\
\verb+\sampi+ & \textgreek{\sampi}\\
\verb+\stigma+ & \textgreek{\stigma}\\
\hline
\end{tabular}
\end{center}
Apart from these symbols there are few more available:
\begin{center}
\begin{tabular}{cc}\hline
Command & Output\\ \hline
\verb+\Digamma+ & \sg\textgreek{\Digamma}\\
\verb+\ddigamma+ & \sg\textgreek{\ddigamma}\\
\verb+\vardigamma+ & \sg\textgreek{\vardigamma}\\
\verb|\euro| & \sg\textgreek{\euro}\\
\verb|\permill| & \sg\textgreek{\permill}\\
\hline
\end{tabular}
\end{center}

In traditional Greek typography the first paragraph after a header is
always indented, contrary to the habit of, say, American typography. This
effect can be achieved by using the package \verb+indentfirst+.

The package \verb|athnum| provides the command \verb|\athnum|, with which
one can produce the so called \textit{Athenian numerals}:
\begin{center}
\begin{tabular}{cc}\hline
Command & Output\\ \hline
\verb|\athnum{1997}| & \sg\textgreek{\athnum{1997}}\\
\hline
\end{tabular}
\end{center}

The package \verb|grmath| renames the basic log-like functions with their
greek counterparts:
\begin{center}
\begin{tabular}{cc}\hline
Command & Output\\ \hline
\verb|$\sin^{2}x+\cos^{2}x=1$| & $\sin^{2}x+\cos^{2}y=1$\\
\hline
\end{tabular}
\end{center}
\end{document}