Definite Articles

The Greek article is a little declinable word which has three genders: masculine, feminine and neuter.
The definite articles in Greek change depending on gender, number and case with the noun
they refer to.

The definite article is used when:

1. The speaker refers to a person, animal or object which is known or has been previously introduced, for example:
Διαβάζω το βιβλίο που μου έδωσες. – I am reading the book you gave me.

2. The speaker speaks generally and refers to a group of similar things or a whole species,
for example:
Το λιοντάρι είναι ο βασιλιάς των ζώων. – The lion is the king of the animals.

Rules

If the following word starts from one of the following letters or letter combinations then you must add the final ν in the accusative case. So the article becomes (την, τον)
α, ε, η, ι, ο, υ, ω, αι, ει οι, ου, υι
κ, π, τ, ξ, ψ, μπ, ντ, γκ, τζ, τσ

If the following word starts from one of the following letters then you must not add ν in the accusative case. So the article becomes (τη, το).
β, γ, δ, ζ, θ, λ, μ, ν, ρ, σ, φ, χ

It is very common, that this rule is not followed by all linguists and some of them are in favor of keeping the final ν in all the masculine words in order to distinguish them from the neuter ones.

Let's see some examples about τη/την:

1. η -> τη
η δασκάλα (teacher-woman) -> τη δασκάλα
η θάλασσα (sea) -> τη θάλασσα
η μητέρα (mother) -> τη μητέρα

2. η -> την
η Ελλάδα (Greece) -> την Ελλάδα
η πάπια (duck) -> την πάπια
η ντουλάπα (closet) -> την ντουλάπα

and some examples about τo/τoν:

1. o -> τo
ο γέρος (old man) -> το γέρο
ο βράχος (rock) -> το βράχο
ο στόχος (target) -> το στόχο

2. o -> τoν
ο αέρας (wind) -> τον αέρα
ο ξένος (stranger) -> τον ξένο
ο καιρός (weather) -> τον καιρό

Below are some examples that show how the noun is formed depending on the gender, number and case

Masculine: ο γιατρός (the doctor)

Singular

Nominative Case --> ο γιατρός
Genitive Case --> του γιατρού
Accusative Case --> το γιατρό

Plural

Nominative Case --> οι γιατροί
Genitive Case --> των γιατρών
Accusative Case --> τους γιατρούς

Feminine: η αδελφή (the sister)

Singular

Nominative Case --> η αδελφή
Genitive Case --> της αδελφής
Accusative Case --> την αδελφή

Plural

Nominative Case --> οι αδελφές
Genitive Case --> των αδελφών
Accusative Case --> τις αδελφές

Neuter: το σπίτι (the house)

Singular

Nominative Case --> το σπίτι
Genitive Case --> του σπιτιού
Accusative Case --> το σπίτι

Plural

Nominative Case --> τα σπίτια
Genitive Case --> των σπιτιών
Accusative Case --> τα σπίτια