Does anyone know how to create numbering for Theorem/lemma/… like this one in the image below, also any idea about the font name?

Does anyone know how to create numbering for Theorem/lemma/… like this one in the image below, also any idea about the font name?

Partial answer that addresses:
Dropped captital/number is solved by package lettrine. It also provides the small caps for Bezeichnungen:.
Color of the number (gray).
Alignment of the equation system (using environment alignat* of package amsmath. Just for fun I have added additional alignments for | and \in.
Letter spacing of the small caps text via \textls of package microtype.
As vertical bar \mid is used, see also question "\mid, | (vertical bar), \vert, \lvert, \rvert, \divides".
Also I have enlarged the number a bit for a better aligment with the top of the text.
\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage[T1]{fontenc}
\usepackage[sc]{mathpazo}
\usepackage{tgpagella}
\usepackage{microtype}
\usepackage{amsmath}
\usepackage{lettrine}
\usepackage{xcolor}
\definecolor{theoremgray}{gray}{.5}
\setlength{\textwidth}{.85\textwidth}% just for reproducing the example
\begin{document}
\lettrine[
loversize=.11,
findent=0.5em,
nindent=0pt,
]{\textcolor{theoremgray}{1.1.1}}{\textls{Bezeichnungen:}}
Ist $G$ eine (multiplikativ geschriebene) Gruppe, so f"uhrt man
f"ur beliebige $g \in G$ und $M, N \subseteq G$ die Bezeichnungen
\begin{alignat*}{4}
&Mg &&= \{mg &&\mid m &&\in M\},\\
&gN &&= \{gn &&\mid n &&\in N\},\\
&MN &&= \{mn &&\mid m &&\in M, n \in N\}
\end{alignat*}
\end{document}
Missing:
Wrapping the visual markup into proper logical markup by defining a theorem style and setting up a theorem, for example.
The answer of Henri Menke shows this using package ntheorem as example.
\usepackage[sc]{mathpazo} for true small caps (and better kerning).
– NauC
May 21 '13 at 07:12
\textls of package microtype for letter spacing.
– Heiko Oberdiek
May 21 '13 at 12:19
align* from amsmath -- the original example shows the left-hand side aligned flush left. can probably be done with alignat* but i haven't tried.
– barbara beeton
May 21 '13 at 14:04
| closes up the spacing more than appropriat. maybe \mid instead of |? (anyhow, nice "drop cap" for the theorem number.)
– barbara beeton
May 21 '13 at 15:12
Remarks
I reproduced Heiko's answer using ntheorem. There is a tricky thing about it: You can't wrap the \lettrine into the [] of the \item as one would normally do for theorems. I get the error
! Argument of \@lettrine has an extra }.
if I do this. I don't know why, maybe somebody knows (Please comment).
Implementation
\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage[T1]{fontenc}
\usepackage[sc]{mathpazo}
\usepackage{tgpagella}
\usepackage{microtype}
\usepackage{amsmath}
\usepackage{lettrine}
\usepackage{xcolor}
\usepackage{ntheorem}
\definecolor{theoremgray}{gray}{.5}
\makeatletter
\newtheoremstyle{mytheorem}%
{\item[]\theorem@headerfont \lettrine[loversize=.11,findent=0.5em,nindent=0pt]{\textcolor{theoremgray}{##2}}{\textls{##1\theorem@separator}} }%
{\item[]\theorem@headerfont \lettrine[loversize=.11,findent=0.5em,nindent=0pt]{\textcolor{theoremgray}{##2}}{\textls{##3\theorem@separator}} }
\makeatother
\theoremstyle{mytheorem}
\theoremheaderfont{\normalfont}
\theorembodyfont{\normalfont}
\theoremseparator{:}
\newtheorem{theorem}{Theorem}[subsection]
\setlength{\textwidth}{.85\textwidth}% just for reproducing the example
\begin{document}
\section{Sectiontitle}
\subsection{Subsectiontitle}
\begin{theorem}[Bezeichnungen]
Ist $G$ eine (multiplikativ geschriebene) Gruppe, so f"uhrt man
f"ur beliebige $g \in G$ und $M, N \subseteq G$ die Bezeichnungen
\begin{alignat*}{4}
&Mg &&= \{mg &&\mid m &&\in M\},\\
&gN &&= \{gn &&\mid n &&\in N\},\\
&MN &&= \{mn &&\mid m &&\in M, n \in N\}
\end{alignat*}
\end{theorem}
\end{document}
Output
ntheorem user manual states, that it is incompatible with amsthm. Some of the features of amsthm are implemented in ntheorem and loading it with \usepackage[amsthm]{ntheorem} will emulate them (It will provides the environments plain, defintion, remark and proof). Conclusion: You can't use ntheorem and amsthm at once. (I would stick with ntheorem instead)
– Henri Menke
May 21 '13 at 20:40
Partial solution: the font is loaded with the package mathpazo.

\usepackage{mathpazo}.
– Sigur
May 21 '13 at 03:11
mathpazoortgpagella. When using XeLaTeX or LuaLaTeX you could also load "Palatino Linotype" (ships with Windows), "TeX Gyre Pagella", "FPL Neu", just to name a few. – Tobias Schula May 23 '13 at 16:00