Мне нравится этот тёплый свитер.

Because Russian expresses this idea differently from English.

Мне нравится X literally works more like X is pleasing to me.

• мне = to me (dative case)
• нравится = is pleasing / appeals
• этот тёплый свитер = this warm sweater

So the person who experiences the liking goes in the dative, not the nominative.

Compare:

• Мне нравится этот свитер. = I like this sweater.
• Ему нравится музыка. = He likes music.
• Нам нравится Россия. = We like Russia.

Because the verb agrees with the thing being liked, not with мне.

In Мне нравится этот тёплый свитер, the subject is этот тёплый свитер = this warm sweater, which is singular. So the verb is singular:

• нравится = singular

If the thing liked were plural, you would use нравятся:

• Мне нравятся эти тёплые свитера. = I like these warm sweaters.

So:

• singular thing → нравится
• plural things → нравятся

Мне is the dative case form of я.

The basic forms are:

• я = I
• мне = to me

The verb нравиться normally uses the dative for the person who likes something:

• мне нравится = I like
• тебе нравится = you like
• ему / ей нравится = he/she likes

This is one of the most important patterns to memorize as a whole:

• кому? нравится что?
• to whom is what pleasing?

It is in the nominative case.

That is because it is the grammatical subject of the sentence — the thing that is pleasing.

You can see the agreement:

• этот = masculine singular nominative
• тёплый = masculine singular nominative
• свитер = masculine singular nominative

All three words match each other in gender, number, and case.

Because свитер is:

• masculine
• singular
• here in the nominative

So the demonstrative must match it:

• masculine nominative singular → этот

Compare:

• этот свитер = this sweater (masculine)
• эта рубашка = this shirt (feminine)
• это пальто = this coat (neuter)
• эти свитера = these sweaters (plural)

Because adjectives in Russian must agree with the noun they describe.

Свитер is masculine singular nominative, so the adjective must also be masculine singular nominative:

• тёплый свитер = warm sweater

Other forms would be used with different nouns:

• тёплая куртка = warm jacket
• тёплое пальто = warm coat
• тёплые вещи = warm clothes

Ё is a separate letter in Russian, and it shows that the syllable is pronounced with a yo sound:

• тёплый ≈ TYOP-liy

In many printed texts, Russians often write е instead of ё, so you may see:

• теплый

But it still means the same word, and it is usually understood from context. For learners, writing ё is very helpful because it shows the correct pronunciation and stress.

The main stress pattern is:

• Мне́ нра́вится э́тот тёплый сви́тер.

Word by word:

• мне́
• нра́вится
• э́тот
• тёплый (stress is naturally on ё)
• сви́тер

Stress is important in Russian, because it is not always predictable.

Yes. Russian word order is more flexible than English word order.

The neutral, natural version is:

• Мне нравится этот тёплый свитер.

But you could also hear:

• Этот тёплый свитер мне нравится.
• Этот свитер мне нравится.

These versions may shift emphasis:

• Мне нравится этот тёплый свитер. → neutral
• Этот тёплый свитер мне нравится. → focuses more on this warm sweater

Even though word order can change, the case endings still show the grammatical roles.

Yes, but it means something slightly different.

• Мне нравится этот тёплый свитер = I like this warm sweater.
• Я люблю этот тёплый свитер = I love this warm sweater.

Любить is usually stronger than нравиться.

So if you just want to say you like it, мне нравится is the more natural choice.

In the present tense, Russian usually does not use a separate word for is/am/are in ordinary sentences.

So Russian says:

• Мне нравится этот свитер.

not something like:

• Мне есть нравится... ❌

The verb нравится already carries the needed meaning. Russian often leaves out the present-tense equivalent of to be.

Usually, no, if you want to say I like.

• Мне нравится этот тёплый свитер. = I like this warm sweater.

If you remove мне, you get:

• Нравится этот тёплый свитер.

That can work only in certain contexts, where to whom is understood from the situation, like casual conversation. But by itself it sounds incomplete to a learner.

So normally, keep мне.

Yes, that is the usual pattern.

Most Russian nouns that end in a consonant in their dictionary form are masculine, and свитер follows that pattern:

• свитер = masculine

That is why you get:

• этот свитер
• тёплый свитер

This rule has some exceptions in Russian, but it works well for most nouns of this type.

You would change the subject phrase to plural, and the verb would also become plural:

• Мне нравятся эти тёплые свитера. = I like these warm sweaters.

Changes:

• нравится → нравятся
• этот → эти
• тёплый → тёплые
• свитер → свитера

This is a very useful pattern to compare with the singular sentence.