Almost everything in Janka's answer is correct, I just want to add something:
Quote from your question:
Every German noun does belong to one of the three genders: Masculine, Feminine or Neuter .
This is not 100% correct. Correct is:
Every German noun does belong to at least one of the three genders ...
This is because there are nous that can be used with two or even all three genders. Here on stackexchange is a still incomplete list of German multigender nouns.
Another addendum:
Adjectives can be used in three different ways:
- attributive
Das schnelle Auto gehört meiner Tante.
The fast car belongs to my aunt.
- predicative
Das Auto ist schnell.
The car is fast.
- adverbial
Das Auto fährt schnell.
The car moves fast.
In attributive usage, it is part of the nominative phrase, whose core is the noun that is described by the adjective. And this is the only situation when an adjective is inflected.
In predicative usage, it still describes a property of a noun, but it does so from a place outside of the nouns nominal phrase. The adjective is bound to its nouns by a copula (a coupling verb). Copulas are verbs, that do not describe an action, but a connection between two things. Copulas are: »sein« (to be), »werden« (to become) and »bleiben« (to stay). Also some other German verbs often act like copulas.
If an adjective is used adverbial, it does not describe a property of a noun, but a property of a verb, a participle or even of another adjective. Janka already explained that difference with »frisch aufgebrühten Tee« and »frischen aufgebrühten Tee«. Here is another example:
- attributive usage (the adjective is inflected)
The car is fast and it also is repaired. »Schnell«/»fast« is a property of the noun »Auto«/»car«:
Das schnelle repariere Auto gehört meiner Tante.
The fast repaired car belongs to my aunt.
- adverbial usage (the adjective is not inflected)
The car is not fast, but it has been repaired quickly. (The repair process took very little time). »Schnell«/»quickly« is a property of the participle »reparierte«/»repaired«:
Das schnell reparierte Auto gehört meiner Tante.
The quickly repaired car belongs to my aunt.
Most important addendum:
Adjectives and verbs that are nominalized (i.e. used as nouns) are nouns (and therefore written with an uppercase first letter), but they do NOT have a fixed gender. They can appear in all three genders. If these words describe persons, the grammatical gender is inherited from the person's sexus.
Examples:
The German word »blond« is an adjective, meaning »blond« or »blonde«.
- attributive usage
male person -> masculine: Der blonde Mann ist müde.
female person -> feminine: Die blonde Frau ist müde.
child -> neuter: Das blonde Kind ist müde.
- predicative usage
Der Mann ist blond und müde.
Die Frau ist blond und müde.
Das Kind ist blond und müde.
- adverbial usage
Der müde Mann färbt sein Haar blond.
Die müde Frau färbt ihr Haar blond.
Das müde Kind färbt sein Haar blond.
- nominalized
Der Blonde ist müde.
Die Blonde ist müde.
Das Blonde ist müde. (rare)
But note, that sometimes an adjective is used in a very similar construction but stays an adjective without being nominalized (and therefore is written all lowercase). This is the case, if it stays an attribute of a noun that exists in the context. (This is the point, where Janka's answer is wrong. This is correct: »Im Wald gibt es viele Bäume. Der große dort hinten ist sehr alt.«)
It is not necessary, that noun and adjective appear in the same sentence. In such a case, they even don't need to match in grammatical number (singular/plural):
Am Nachbartisch sitzen zwei Männer. Der blonde ist müde.
Am Nachbartisch sitzen zwei Frauen. Die blonde ist müde.
Am Nachbartisch sitzen zwei Kinder. Das blonde ist müde.
In fact in such a construction, the second sentence is a coordination ellipsis (German: Koordinationsellipse). An ellipsis is a sentence where a part is omitted, that easily can be reconstructed by the listener or reader.
- full versions:
Am Nachbartisch sitzen zwei Männer. Der blonde Mann ist müde.
Im Wald gibt es viele Bäume. Der große Baum dort hinten ist sehr alt.
- elliptic versions:
Am Nachbartisch sitzen zwei Männer. Der blonde ist müde.
Im Wald gibt es viele Bäume. Der große dort hinten ist sehr alt.