The German Genitiv is quite similar to the English one,
though it works the other way round.
"The man's house." Das Haus des Mannes.
Male and neuter nouns attach an "s", usually preceded by an euphonic "e":
der Mann: des Mannes
das Pferd: des Pferdes.
As in English, we have an alternative form using a preposition with Dativ.
"The house of the man."
Das Haus von dem (vom) Mann.
This is not considered very elegant.
The articles are:
des/ eines, der/ einer,
des/ eines. Plurals: der/ --
Now you can easily understand one of the central constuctions of our book titles:
Die Phänomenologie des Geistes
Der Untergang des Abendlandes
Die Kritik der reinen Vernunft
The latter case is particularly interesting. As Kant himself states, the title can be understood
as
"critique of pure reason" (the object of the critique) or as
"critique by pure reason" (the subject of the critique).