Tässä on uusi kirja, ole hyvä.

Tässä means here in this sentence.

Literally, it is the inessive form of tämä (this), so its basic idea is in this or at this. In everyday Finnish, though, tässä is very often used simply to mean here:

• Tässä on kirja. = Here is a book.
• Olen tässä. = I’m here.

So in Tässä on uusi kirja, tässä introduces something as being here / here you are.

On is the third-person singular form of olla (to be), so it means is.

So the structure is basically:

• Tässä = here
• on = is
• uusi kirja = a new book / the new book

Together: Here is a new book.

Finnish uses olla very often in this kind of sentence, just as English uses is.

Finnish has no articles, so there is no direct equivalent of a/an or the.

Because of that, uusi kirja can mean:

• a new book
• the new book

Which one is meant depends on the context. In this sentence, English would usually translate it as a new book or here is the new book, depending on the situation.

This is very normal in Finnish: nouns appear without articles.

Because here the noun phrase is in the nominative singular, the basic dictionary form:

• uusi = new
• kirja = book

In this sentence, uusi kirja is what is being presented: Here is a new book.

Finnish changes noun forms a lot depending on grammar, but after on in a simple sentence like this, the basic nominative form is often used.

For comparison:

• Tässä on uusi kirja. = Here is a new book.
• Minä ostin uuden kirjan. = I bought a new book.

So uuden kirjan appears in a different grammatical role.

Yes. In Finnish, adjectives usually agree with the nouns they describe in number and case.

Here both words are in the singular nominative:

• uusi = new
• kirja = book

So they match: uusi kirja

In another case, both would change:

• uuden kirjan = of a new book / a new book (object in some contexts)
• uudessa kirjassa = in a new book

So agreement is an important feature of Finnish grammar.

Starting with tässä makes the sentence feel like presenting or offering something:

• Tässä on uusi kirja. = Here is a new book.

This is very natural when you are showing or handing something to someone.

If you say:

• Uusi kirja on tässä.

that sounds more like:

• The new book is here.

So the word order changes the emphasis:

• Tässä on uusi kirja → presenting the book
• Uusi kirja on tässä → talking about the location of the book

Finnish word order is more flexible than English, but different orders often shift the focus.

Ole hyvä is an idiomatic expression. In this sentence it means something like:

• here you are
• please
• there you go

It is commonly used when giving something to someone.

So:

• Tässä on uusi kirja, ole hyvä.

can be understood as:

• Here is a new book, here you are.
• Here is a new book, please.

It can also mean you’re welcome in other contexts, especially after someone says kiitos (thank you).

Because ole hyvä uses the imperative form of olla (to be):

• ole = be (command/request to one person)

So literally ole hyvä means something like be good or be kind, but that literal meaning is not how it is usually understood. It functions as a fixed polite phrase.

By contrast:

• olet hyvä = you are good

That is just a normal statement, not the expression used when handing something over.

The basic form ole hyvä is for one person.

If you are speaking to several people, Finnish uses:

• olkaa hyvä

This is the plural/polite form.

So:

• Ole hyvä. = said to one person
• Olkaa hyvä. = said to several people, or sometimes politely to one person in formal situations

The comma separates two parts:

• Tässä on uusi kirja
• ole hyvä

The second part is a kind of added polite expression, almost like an inserted phrase: here you are / please.

In English, you might also separate this kind of thing with punctuation:

• Here is a new book, please.
• Here is a new book — here you are.

So the comma helps mark the pause between the main statement and the polite expression.

Yes, absolutely.

• Tässä on uusi kirja. = Here is a new book.

That is already a complete sentence.

Adding ole hyvä makes it sound more polite and more natural in a situation where you are actually handing or presenting the book to someone.

So:

• Tässä on uusi kirja. = simple statement
• Tässä on uusi kirja, ole hyvä. = statement + polite offering

Tässä is pronounced approximately TAHSS-sah, with the stress on the first syllable, because Finnish stress normally falls on the first syllable of the word.

A few helpful points:

• ä is not the same as English a
• ss is a long/double s
• both syllables are pronounced clearly: täs-sä

Finnish spelling is very regular, so pronunciation usually matches the written form closely.

Yes. That often surprises English speakers.

Ole hyvä is used in at least two very common situations:

• when giving something to someone: here you are / please
• after kiitos: you’re welcome

So context tells you which meaning is intended.

In your sentence, because someone is presenting a book, ole hyvä means here you are / please, not you’re welcome.