Adjectival nouns are nouns formed directly from adjectives. Here are some examples in English:
The meek shall inherit the earth. Which one should I wear? The red or the blue?
Adjectival nouns, though perfectly correct, are relatively rare in English. Usually speakers repeat the noun, or substitute the word "one" where an adjectival noun might occur. In the last example, many English speakers would say, "the red one or the blue one?"
Adjectival nouns are more common in German, and are frequently used to describe objects, especially when it is needed to contrast with another object. Adjectival nouns can also refer to people, when done so politely.
Adjectival nouns in German are formed and declined the same way attributive adjectives are, except that in the M, N Genitive Singular, they add an s. They are usually capitalized.
M (the small man) N (the small object) F (the small woman) Pl (the small beings)
Definite Article and der-words
der Kleine das Kleine die Kleine die Kleinen den Kleinen das Kleine die Kleine die Kleinen dem Kleinen dem Kleinen der Kleinen den Kleinen des Kleinens des Kleinens der Kleinen der Kleinen
Indefinite Article and ein-words
ein Kleiner ein Kleines eine Kleine keine Kleinen einen Kleinen ein Kleines eine Kleine keine Kleinen einem Kleinen einem Kleinen einer Kleinen keinen Kleinen eines Kleinens eines Kleinens einer Kleinen keiner Kleinen
Adjectival nouns without an article are very rare, except in the plural, and follow the strong declension pattern.
There are two small points that need to be noted:
1) The attributive adjective "ander-" (other) is not capitalized when it forms an adjectival noun. It is declined as above. "Ich gehe mit den anderen", or, I am going with the others.
2) Almost all nationalities have nouns associated with them, e.g., "der Franzose/die Französin", "der Amerikaner/die Amerikanerin", and one should always use these nouns instead of forming adjectival nouns with their associated adjectives.
The one exception to this is, strangely, "Deutsch", which does not have a nominal form akin to those above. The German man is "der Deutsche"; a German man is "ein Deutscher"; a German woman is "eine Deutsche"; the Germans are "die Deutschen"; and so on. The adjective is declined as above.
Remember, in the previous example, "die Deutsche" is capitalized because it is an adjectival noun, not because it is a proper noun, which in English would require it to be capitalized. As with all other adjectives, when "deutsch" is used as an attributive or predicate (separated with a verb such as "sein") adjective, it should be lower-case: "die deutschen Frauen", as opposed to "the German women" in English. Note also that predicate adjectives are uninflected: "Er ist deutsch/krank/schwul/etc."