Prema ovoj mapi, muzej je blizu reke.

Here prema means according to.

So Prema ovoj mapi = According to this map.

A useful thing to know is that prema can also mean toward / in the direction of in other sentences, so context matters:

• Idemo prema centru = We are going toward the center.
• Prema ovoj mapi... = According to this map...

Because prema requires the dative case.

The basic form is:

• ova mapa = this map

But after prema, both words change to dative singular:

• ova → ovoj
• mapa → mapi

So:

• prema ovoj mapi = according to this map

Because blizu normally goes with the genitive case.

The basic form is:

• reka = river

After blizu, it becomes:

• reke = of the river / near the river

So:

• blizu reke = near the river

This is very common in Serbian:

• blizu škole = near the school
• blizu grada = near the city

For a learner, the easiest way to treat blizu is as a word meaning near / close to that is followed by the genitive.

In this sentence:

• blizu reke = near the river

You do not need a separate word for to as in English close to. Serbian just uses blizu + genitive.

Because Serbian does not have articles like a or the.

So:

• muzej can mean a museum or the museum
• reka / reke can mean a river / the river, depending on context

If Serbian wants to be more specific, it often uses context or words like:

• ovaj = this
• taj = that

In your sentence, ovoj mapi already means this map, but muzej and reke are understood from context.

Because Serbian normally keeps the present tense of to be:

• je = is

So:

• muzej je blizu reke = the museum is near the river

This is different from some other Slavic languages where the present tense of to be may be omitted. In standard Serbian, je is needed here.

Yes. Serbian word order is more flexible than English.

The neutral, natural order here is:

• Muzej je blizu reke.

But other orders are possible for emphasis, for example:

• Blizu reke je muzej. = It is near the river that the museum is.
• Prema ovoj mapi, blizu reke je muzej.

Even though word order can move, the cases still show the grammatical relationships, so the meaning usually remains clear.

Muzej is in the nominative singular because it is the subject of the sentence.

So the structure is:

• muzej = subject
• je = is
• blizu reke = near the river

Dictionary form:

• muzej = museum

Because it agrees with mapi, and mapa is a feminine noun.

In Serbian, words like this must match the noun in:

• gender
• number
• case

So here:

• mapa = feminine singular
• after prema it must be dative singular
• therefore ovaj becomes ovoj

Yes. That depends on the regional standard.

Your sentence uses the Ekavian form:

• reka
• reke

In Ijekavian, you would hear:

• rijeka
• rijeke

So both are correct, depending on the variety of Serbian:

• Prema ovoj mapi, muzej je blizu reke.
• Prema ovoj mapi, muzej je blizu rijeke.