Learn Hardcore Greek: Η κάλτσα μου είναι μπλε.

Η → i (like English ee in see)
κάλ-τσα → KÁL-tsa (stress on κάλ; τσ like ts in cats)
μου → mu (like moo but shorter)
εί-ναι → Í-ne (stress on εί)
μπλε → ble (like bleh but without the final h sound; μπ here sounds like b)

Why is it η κάλτσα and not ο κάλτσα or το κάλτσα?

Greek nouns have grammatical gender: masculine, feminine, or neuter. The definite article must agree with the noun in gender, number, and case.

η = feminine singular nominative
ο = masculine singular nominative
το = neuter singular nominative

The noun κάλτσα (sock) is grammatically feminine, so it takes the feminine article η.

A very common pattern is that many feminine nouns end in -α (like κάλτσα, πόρτα, γλώσσα), and they normally use η in the nominative singular.

What exactly does μου mean here?

μου is a weak possessive pronoun meaning my (literally of me).

It is in the genitive case.
It is clitic (unstressed and normally written without its own accent).
In this position (after a noun), it expresses possession.

So η κάλτσα μου literally means the sock of-me, i.e. my sock.

Why does μου come after the noun, instead of before it like English my sock?

In Greek, the normal and most common way to say my X is:

article + noun + weak possessive pronoun

So:

η κάλτσα μου = my sock
το σπίτι μου = my house
ο φίλος μου = my friend

Putting μου after the noun is the standard pattern with these weak possessives (μου, σου, του, της, μας, σας, τους).

Greek can say something closer to English word order, but it uses a different construction, e.g.:

η δική μου κάλτσα or η δικιά μου κάλτσα = my own sock / the sock that is mine (more emphasis on my).

Can μου ever be written before the noun, like μου η κάλτσα?

In modern standard Greek, you do not normally put μου directly before the noun like that.

✗ μου η κάλτσα is wrong or at best sounds very unnatural in modern speech.

To put a stressed my before the noun, you use δικός/δική/δικό plus μου, for example:

η δική μου κάλτσα or η δικιά μου κάλτσα = my sock (as opposed to someone else’s)

So the practical rule: with simple possession, keep μου after the noun: η κάλτσα μου.

What does είναι mean, and how is it related to είμαι?

είναι is a form of the verb είμαι (to be).

είμαι = I am
είναι = he is / she is / it is / they are

So in η κάλτσα μου είναι μπλε, είναι corresponds to English is.

Greek uses είναι both for is and are, depending on context:

η κάλτσα μου είναι μπλε = my sock is blue
οι κάλτσες μου είναι μπλε = my socks are blue

Where is the subject pronoun it in Greek? Why doesn’t the sentence include it?

Greek usually omits subject pronouns when the subject is clear from the verb form and the context.

In this sentence:

The subject is η κάλτσα μου (my sock).
The verb είναι tells us we are talking about he/she/it/they.
A separate it is not needed.

Greek does have a word that can function like it (αυτό in the neuter), but you would not normally use it here. Saying something like:

Αυτή η κάλτσα μου είναι μπλε = This sock of mine is blue

is possible, but now you are saying this sock rather than just my sock.

Why doesn’t μπλε change form to agree with the feminine noun κάλτσα?

Many Greek adjectives do change form for gender, number, and case, for example:

κόκκινος (m), κόκκινη (f), κόκκινο (n) = red
→ η κόκκινη κάλτσα = the red sock

But μπλε (blue) is one of several adjectives that are indecinable in modern Greek:

μπλε stays the same form for masculine, feminine, and neuter, singular and plural.

So you have:

η κάλτσα είναι μπλε = the sock is blue (feminine singular)
το φόρεμα είναι μπλε = the dress is blue (neuter singular)
οι κάλτσες είναι μπλε = the socks are blue (feminine plural)

In all cases, μπλε does not change.

What do the accent marks in κάλτσα and είναι tell me?

The written accent (´) in Greek marks the stressed syllable of the word.

κάλτσα → stress on the first syllable: ΚÁL-tsa
είναι → stress on the first syllable: Í-ne

Every word of two or more syllables normally has one accent mark to show where the stress falls. Correct stress is important for Greek pronunciation and sometimes for distinguishing different words.

How would I say My socks are blue in Greek?

You make the noun and article plural, but the rest of the sentence stays the same:

η κάλτσα μου είναι μπλε = my sock is blue
οι κάλτσες μου είναι μπλε = my socks are blue

Changes:

η → οι (feminine plural nominative article)
κάλτσα → κάλτσες (plural of κάλτσα)

μου and μπλε do not change, and είναι covers both is and are.

Can I omit the article and just say Κάλτσα μου είναι μπλε?

No, that is not normal in standard modern Greek.

With possessive pronouns like μου, you almost always use the definite article:

η κάλτσα μου είναι μπλε ✔️ natural
κάλτσα μου είναι μπλε ✗ sounds wrong/very odd

Think of article + noun + possessive as the default pattern for my/your/his/her/our/their + noun in Greek.

Does κάλτσα only mean sock, or does it have other common meanings?

In modern everyday Greek, κάλτσα mainly means sock, as in the clothing item you wear on your foot.

You might also see:

καλτσάκι = little sock / small sock (diminutive)
κάλτσες = socks (plural)

It is not typically used with other figurative meanings in the way English sometimes uses sock metaphorically.