Tämä villatakki on vanha mutta lämmin.

Tämä means this. It is a demonstrative pronoun, used to point out a specific thing.

In Tämä villatakki on vanha mutta lämmin, tämä comes first because it introduces the subject: this cardigan / this wool sweater.

Finnish often puts the subject near the beginning of a basic statement, just like English:

• Tämä villatakki = this cardigan
• on = is
• vanha mutta lämmin = old but warm

So the structure is very straightforward.

Villatakki is a compound word:

• villa = wool
• takki = coat, jacket, outer garment

Together, villatakki usually means cardigan or wool jacket/sweater, depending on context.

Compound words are extremely common in Finnish, so it is useful to get used to breaking them into parts.

Finnish does not have articles like English a/an and the.

So villatakki can mean:

• a cardigan
• the cardigan
• just cardigan

The exact meaning depends on context.

Here, tämä already makes it specific, so tämä villatakki clearly means this cardigan.

On is the 3rd person singular form of the verb olla, which means to be.

So:

• minä olen = I am
• sinä olet = you are
• hän on = he/she is
• tämä villatakki on = this cardigan is

In this sentence, on links the subject to the descriptions vanha and lämmin.

They are in their basic dictionary form because they are predicate adjectives after the verb olla (to be).

In English, we say:

• The cardigan is old
• The cardigan is warm

Finnish works similarly:

• Villatakki on vanha
• Villatakki on lämmin

The adjectives do not need a special ending here. They match the singular subject in a basic way.

Mutta is the normal Finnish word for but in statements like this.

So:

• vanha mutta lämmin = old but warm

It connects two contrasting qualities:

• it is old
• but it is also warm

This is very similar to English usage.

Here, both tämä and villatakki are in the nominative because the phrase is the subject of the sentence.

So:

• tämä villatakki = this cardigan

Finnish changes words a lot in other cases, but in a simple X is Y sentence, the subject is usually in the nominative.

For example:

• Tämä villatakki on uusi. = This cardigan is new.
• Tämä talo on suuri. = This house is big.

The basic neutral word order is:

Tämä villatakki on vanha mutta lämmin.

That is the most natural version for a learner to use.

Finnish word order is more flexible than English, and changing the order can change emphasis. For example, a different order might highlight one part more strongly. But the standard, unmarked order is:

• subject
• verb
• description

So this sentence is a good model to follow.

Yes. Lämmin is the normal dictionary form of the adjective meaning warm.

Some Finnish adjectives have stems that change when inflected, and lämmin is one of them. For example, in other forms you may later see:

• lämpimä- as part of the stem

But in this sentence, you only need the basic form:

• lämmin = warm

So even if it looks a little unusual at first, this is the correct standard form.

A few helpful points:

• v is like English v
• i is like ee in see
• ä is a front vowel, somewhat like the a in some pronunciations of cat, but not exactly the same
• double consonants are pronounced longer in Finnish

So:

• villatakki has a long ll and long kk
• lämmin has a long mm

Roughly:

• vil-la-tak-ki
• läm-min

In Finnish, vowel and consonant length matters, so saying the double consonants clearly is important.

Yes, but it means something slightly different in structure.

• Tämä villatakki on vanha mutta lämmin.
  = This cardigan is old but warm.

• Tämä on vanha mutta lämmin villatakki.
  = This is an old but warm cardigan.

In the first sentence, old and warm are predicate adjectives describing the cardigan after is.

In the second sentence, vanha mutta lämmin comes before villatakki and works more like an adjective phrase directly modifying the noun.

Both are correct, but they are built differently.

In Finnish, a comma is usually not needed before mutta when it connects just two simple adjectives or descriptions within a short clause like this.

So:

• Tämä villatakki on vanha mutta lämmin.

That is the normal way to write it.

If you had longer or more complex clauses, comma rules would become more important, but in this sentence the plain version without a comma is natural and standard.