Ancient Greek nouns are words for people, beings, things, places, phenomena, qualities or ideas. They have much in common with those of the ancestral Proto-Indo-European language, such as the high quantity of inflections.
The main form of any Ancient Greek noun is the singular nominative. Other variations can be achieved through declension in case and number, according to one of these declension systems: the first declension, the second declension and the third declension.
As in English, the singular form indicates a quantity of one. Also, as in English, there is the plural for a quantity of more than one. Ancient Greek goes further, though, with the dual, for a quantity of two.
In English, grammatical relations are mostly shown by word order: for example, "The band hired the singer" and "The singer hired the band" mean completely different things. In Ancient Greek, grammatical relations are shown mostly by grammatical cases.
The nominative case, is used to show the subject of a sentence, the person or thing whose action or existence is being described by the verb.
Objects are what receives the action of the verb. In the English sentence, "I threw him the ball", "the ball" is the direct object: the action of the verb affects it directly. In Ancient Greek, direct objects are in the accusative case. "Him" is the indirect object: the action of the verb also affects it, but less directly. After all, the person referred to by "him" isn't being thrown, only the ball. In Ancient Greek, indirect objects are in the dative.
The genitive case is used to show what something or someone belongs to, either by ownership ("my book"), or relationship ("my teacher"). In English, this is mostly shown by adding "-'s" or using "of", but there are genitive forms for the pronouns.
Ancient Greek also has a vocative case, which shows who or what the speaker or writer of the sentence is talking or writing to.
All Ancient Greek nouns are masculine, feminine or neuter. For people, supernatural beings, and animals, the grammatical gender is often the same as the actual gender: men, boys, and male animals are masculine, while women, girls, and female animals are feminine. There are exceptions, though, and many things that have no gender in English are grammatically masculine or feminine in Ancient Greek. Although there are a few rules and patterns (suffixes often have their own inherent gender, for example), there's usually no apparent reason for which grammatical gender a noun has if it's not referring to people, supernatural beings, or animals.
The grammatical gender and case of nouns is reflected in the grammatical gender and case of the adjectives and articles accompanying them. For instance, for nominative singular nouns, the articles can be masculine ὁ, feminine ἡ or neuter τό. In the first and third declensions, grammatical genders of the nouns may be distinguished through their different declined forms. However, in the second declension, the masculine and feminine forms have all the same declined forms, but you can tell the gender by the articles or adjectives that go with them. The first declension comprises only masculine and feminine nouns.