
kein
no / not any
Negates a noun with an indefinite article (ein/eine) or with no article. It expresses that something is not present or does not apply.
Ich habe leider keinen Stift für dich.
Unfortunately, I don't have a pen for you.
no / not any
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no / not any
Negates a noun with an indefinite article (ein/eine) or with no article. It expresses that something is not present or does not apply.
Ich habe leider keinen Stift für dich.
Unfortunately, I don't have a pen for you.

not a
Used to negate a quality or category and means 'not a' or 'not the kind of'.
Das ist doch kein Problem, ich helfe dir gerne.
That's really not a problem; I'm happy to help you.

not a single
Used for strong emphasis to express that absolutely nothing or no one is affected. Often in the phrase 'kein einziger' (not a single one).
Auf meine Frage kam kein einziges Wort als Antwort.
Not a single word came in response to my question.
The word `kein` (no / not any) is used to negate nouns that appear with `ein`/`eine` (a/an) or with no article in the positive sentence. It is declined like the indefinite article and agrees with the noun in gender, number, and case.
Ich habe einen Hund. → Ich habe keinen Hund.
I have a dog. → I don't have a dog.
In the meaning 'not the kind of', `kein` (not a) is often used in emotional or evaluative statements. It expresses that something does not really deserve the label.
Das ist doch kein richtiges Essen, das ist nur ein Snack!
That's not real food; it's just a snack!
To make a negation absolute, `kein` (no / not any) is often intensified with `einzig` (single). The phrase `kein einziger` / `keine einzige` / `kein einziges` means 'absolutely zero' or 'not a single one'.
Kein einziger Gast hat sich über das Essen beschwert.
Not a single guest complained about the food.
nothing
Nichts and kein both express that something is absent. Nichts stands on its own for an absent thing, whereas kein accompanies an explicitly mentioned noun and is adjusted to match it.

Im Kühlschrank finde ich kein Brot zum Frühstück.
I can't find any bread for breakfast in the refrigerator.
Im Kühlschrank finde ich nichts zum Frühstück.
I can't find anything for breakfast in the refrigerator.