Društvena igra je na stolu.

• društvena = an adjective, meaning social; here it is part of the fixed expression for board game
• igra = game
• je = is, the 3rd person singular present form of biti (to be)
• na = on
• stolu = table in the form required after na when talking about location

So the structure is:

društvena igra + je + na stolu
subject + verb + place

Because they agree with each other.

igra is a feminine singular noun in the nominative case, and the adjective describing it must match:

• gender: feminine
• number: singular
• case: nominative

So:

• društvena igra = feminine singular nominative

If the noun changed, the adjective would change too.

Yes. Društvena igra is the normal Serbian term for board game.

Literally, it looks more like social game, but in actual usage it commonly means a board game or tabletop game played with other people.

So even though the literal pieces may seem a little surprising, learners should usually understand društvena igra as the standard vocabulary item.

Je is the present-tense form of biti (to be) for he/she/it is.

In standard Serbian, you normally keep it:

• Društvena igra je na stolu. = correct

Leaving it out would usually sound incomplete or non-standard in an ordinary sentence.

Because je is a clitic, and Serbian clitics usually come in second position.

That means je often goes after the first full phrase, not necessarily after the first single word.

So:

• Društvena igra je na stolu. = natural

Here, the first unit is the whole noun phrase društvena igra, and je comes right after it.

This is why you do not normally say:

• Društvena je igra na stolu for this neutral meaning

Because Serbian changes the noun depending on whether you mean:

• location = where something is
• direction/movement = where something is going

Here, the game is already on the table, so this is location. After na, location usually takes the locative case:

• na stolu = on the table

But if you were talking about movement onto the table, you would use the accusative:

• Stavljam društvenu igru na sto. = I am putting the board game onto the table.

So:

• na stolu = location
• na sto = movement toward/on to

It is the locative singular form of sto (table).

Basic form:

• sto = table

After na when it means location:

• na stolu = on the table

For this noun, the dative and locative singular have the same form:

• stolu

Because Serbian does not have articles like English a and the.

So Društvena igra je na stolu can mean:

• The board game is on the table
• A board game is on the table

Which one is intended depends on context.

This is very common for English speakers to notice at first: Serbian usually leaves definiteness to the situation, not a separate article word.

Serbian word order is fairly flexible, though some orders sound more neutral than others.

The most neutral version here is:

• Društvena igra je na stolu.

You can also say:

• Na stolu je društvena igra.

That version puts more focus on the location, something like:

• On the table is a board game or
• There is a board game on the table

So yes, the word order can change, but the emphasis changes too.

A rough guide is:

• Društvena ≈ DROOSH-tveh-na
• igra ≈ EE-gra
• je ≈ yeh
• na ≈ nah
• stolu ≈ STO-loo

A few useful notes:

• š sounds like sh
• j sounds like English y
• r in igra is a tapped or rolled Serbian r

So the whole sentence sounds roughly like:

DROOSH-tveh-na EE-gra yeh nah STO-loo

Yes, if the context already makes it clear what kind of game you mean.

• Društvena igra je na stolu. = The board game is on the table.
• Igra je na stolu. = The game is on the table.

The shorter version is perfectly grammatical, but it gives less information.

Absolutely. It is a very useful pattern.

You can swap in other nouns before it:

• Knjiga je na stolu. = The book is on the table.
• Telefon je na stolu. = The phone is on the table.
• Čaša je na stolu. = The glass is on the table.

So a very useful pattern to remember is:

[something] je na stolu = [something] is on the table