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Encyclopedic overview
Latin declension is the set of patterns in the Latin language for how nouns and certain other parts of speech (including pronouns and adjectives) change form according to their grammatical case, number and gender. Words that change form in this manner are said to be declined.
Declension is normally marked by suffixation: attaching different endings to the declined word. For nouns, Latin grammar instruction typically distinguishes five main patterns of endings. The patterns are numbered from first to fifth and subdivided by grammatical gender. The term "declension" can refer either to the overarching phenomenon, or to one of these specific five patterns. For example, nouns that have a genitive singular form that ends in -ae are said to belong to "the first declension".
Excerpted from Wikipedia’s “Latin declension” article, available under the CC BY-SA 4.0 licence.