What are the differences between the various endings of adjectives in German?

In German (unlike in French), adjectives always go before the noun that they are describing. In German, the ending of the adjective has to match both the case, gender, and number of the noun. Take, for example, the feminine noun 'die Katze' (the cat). Looking at the noun you can see that it is both feminine (indicated by the 'die') and it is singular (because of the form of the word ). If it was used in a sentence like so 'die Katze sitzt auf dem Teppich' (the cat sits on the mat), we could then work out the case, whether it is doing the action or not, or is something else. In this example the cat is the subject (actor), and so is in the nominative case. This means that in the sentence 'die schwarz_ Katze sitzt auf dem Teppich' (the cat sits on the mat), the adjectival ending would need to be 'e', because singular, feminine nouns in the nominative case use 'e' on their adjectives. So it would be 'die schwarze Katze sitzt auf dem Teppich'