I just started learning Genitiv. I remember the article 1 of German Basic Law: "Die Würde des Menschen ist unantastbar". I assume Menschen is plural. Why des instead of "der" is used here?
No, it is not plural. It is singular. If it were plural, it would have been
Plural: Die Würde der Menschen ist unantastbar.
The dignity of humans is inviolable.
But it is
Plural: Die Würde des Menschen ist unantastbar.
The dignity of man is inviolable.
This is a rhetoric figure called "synecdoche". Synecdoches appear in various forms. Pars pro toto is a very common form of a synechdote (counting noses instead of counting people).
In German also using singular if you mean all is a form of a synechdote:
Der Deutsche isst gerne Kartoffeln. (means: Deutsche essen gerne Kartoffeln)
The German likes to eat potatoes. (Germans like to eat potatoes.)
There is also to add, that the meaning of this sentence is not the statement "The dignity of man is inviolable". This is not true. Dignity of man can be violated. There are millions of example in human history where die dignity of people have been violated. So, claiming that you can't violate dignity is not the meaning of this sentence.
The real meaning is not a statement but a rule or law:
Die Würde des Menschen darf nicht verletzt werden.
The dignity of man must not be violated.
I assume Menschen is plural.
No, it's singular.
In German, singular with a definite article is sometimes used to make statements that apply to all individuals of a group. This style may sound somewhat old-fashioned nowadays, but it used to be typical in various contexts, e.g. politics (saying "der Franzose" when actually, "the French" are meant) or biology ("Das Krokodil ist ein Fleischfresser.", which is meant as a general statement about all crocodiles).