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+\documentclass[a4paper]{article}
+
+\usepackage[cm]{manuscript}
+\usepackage{xcolor}
+
+\newcommand{\scene}[1]{\noindent[ #1 ]\par}
+\newenvironment{totranslate}{\color{blue!70!black}}{}
+
+\begin{document}
+
+\section{Intro}
+
+\section{Geometrie}
+\begin{totranslate}
+We'll start with geometric symmetries as they are the simplest to grasp.
+
+\scene{Intro}
+  To mathematically formulate the concept, we will think of symmetries as
+  actions to perform on an object, like this square. The simplest action, is to
+  take this square, do nothing and put it back down. Another action could be to
+  flip it along an axis, or to rotate it around its center by 90 degrees.
+
+\scene{Cyclic Groups}
+  Let's focus our attention on the simplest class of symmetries: those
+  generated by a single rotation. We will gather the symmetries in a group
+  \(G\), and denote that it is generated by a rotation \(r\) with these angle
+  brackets.
+  
+  Take this pentagon as an example. By applying the rotation \emph{action} 5
+  times, it is the same as if we had not done anything, furthermore, if we
+  \emph{act} a sixth time with \(r\), it will be the same as if we had just
+  acted with \(r\) once.  Thus the group only contain the identity and the
+  powers of \(r\) up to 4.
+  
+  In general, groups with this structure are known as the ``Cyclic Groups'' of
+  order \(n\), where the action \(r\) can be applied \(n-1\) times before
+  wrapping around. 
+
+  % You can think of them as the rotational symmetries of an \(n\)-gon.
+
+\scene{Dihedral Groups}
+  Okay that was not difficult, now let's spice this up a bit. Consider this
+  group for a square, generated by two actions: a rotation \(r\) and a
+  reflection \(\sigma\). Because we have two actions we have to write in the
+  generator how they relate to each other.
+
+  Let's analyze this expression. Two reflections are the same as the identity.
+  Four rotations are the same as the identity, and a rotation followed by a
+  reflection, twice, is the same as the identity.
+
+  This forms a group with 8 possible unique actions. This too can be generalized
+  to an \(n\)-gon, and is known as the ``Dihedral Group'' of order \(n\).
+\end{totranslate}
+
+\scene{Symmetrische Gruppe}
+\scene{Alternierende Gruppe}
+
+\section{Algebra}
+
+\section{Krystalle}
+
+\end{document}
+% vim:et ts=2 sw=2: