Muzeum je vlevo a knihovna vpravo.

Je is the 3rd person singular present form of the verb být (to be).

So here it means is.

• muzeum je vlevo = the museum is on the left
• knihovna je vpravo = the library is on the right

A useful detail: je is used for he/she/it is, so it does not change according to grammatical gender here.

Because Czech often omits a repeated verb when it is easy to understand from context.

So:

• Muzeum je vlevo a knihovna vpravo.

is a shortened version of:

• Muzeum je vlevo a knihovna je vpravo.

Both are correct. The version without the second je sounds natural and economical.

They are adverbs.

• vlevo = on the left / to the left
• vpravo = on the right / to the right

In this sentence, they describe location.

English uses a longer phrase like on the left, but Czech can express that with just one word.

Because Czech does not have articles.

So muzeum can mean:

• a museum
• the museum

and knihovna can mean:

• a library
• the library

Context tells you which meaning is intended.

They are in the nominative singular because they are the subjects of the sentence.

• muzeum = nominative singular
• knihovna = nominative singular

The words vlevo and vpravo are adverbs, so they are not in a case.

• muzeum is neuter
• knihovna is feminine

That matters in Czech for things like adjectives and pronouns, for example:

• velké muzeum = big museum
• velká knihovna = big library

But in this sentence, the verb form je stays the same.

Yes. That is completely correct.

The difference is mainly style:

• Muzeum je vlevo a knihovna vpravo. = more compact
• Muzeum je vlevo a knihovna je vpravo. = more explicit

Both are natural.

Yes. Czech word order is more flexible than English.

For example, you could also say:

• Vlevo je muzeum a vpravo knihovna.

That version is also very natural, especially if you are describing a layout or what someone sees from left to right.

In general:

• starting with muzeum / knihovna focuses more on the things
• starting with vlevo / vpravo focuses more on the positions

This is a very common question.

• vlevo / vpravo usually describe position
• doleva / doprava usually describe direction of movement

Compare:

• Muzeum je vlevo. = The museum is on the left.
• Jděte doleva. = Go left.

So in your sentence, vlevo and vpravo are the right choice because the sentence describes where things are, not where someone should move.

A rough English-friendly guide is:

• Muzeum ≈ MOO-zeh-um
• je ≈ ye
• vlevo ≈ VLEH-vo
• a ≈ ah
• knihovna ≈ KNI-hov-na
• vpravo ≈ VPRA-vo

A few useful pronunciation notes:

• Czech stress is usually on the first syllable of each word.
• je sounds like ye, not like English jee.
• In knihovna, the k is pronounced. English speakers often want to make it silent because of words like knife, but Czech pronounces it.
• The beginnings vl- and vp- can feel difficult at first; that is normal.

Because a here simply joins two parallel parts of the sentence, like and in English.

So:

• Muzeum je vlevo a knihovna vpravo.

does not need a comma.

In Czech, a comma before a is only used in certain special structures, not in a simple coordination like this one.

Yes. You could say:

• Muzeum je na levé straně a knihovna na pravé straně.

That means more literally The museum is on the left side and the library on the right side.

The original sentence with vlevo and vpravo is shorter and very natural, but this longer version can help learners see the meaning more clearly.