Після дощу тротуар мокрий, і біля світлофора є велика калюжа.

Because після takes the genitive case.

The noun дощ changes in the genitive singular to дощу, so:

• дощ = rain
• після дощу = after the rain

This is a very common pattern in Ukrainian:

• після уроку = after the lesson
• після роботи = after work

So the important thing to remember is:

• після + genitive

It means after the rain or after it has rained.

In this sentence, it sets the scene and explains the situation that follows: the sidewalk is wet and there is a big puddle. So it is mainly a time expression, though it also naturally suggests the cause.

You can think of it as:

• Після дощу = after the rain / once the rain is over

In Ukrainian, the verb to be is usually not expressed in the present tense when linking a subject to an adjective or noun.

So:

• тротуар мокрий literally looks like sidewalk wet
• but it means the sidewalk is wet

This is completely normal Ukrainian.

Compare:

• Він щасливий. = He is happy.
• Кава гаряча. = The coffee is hot.

So in the first part of the sentence, Ukrainian does not need an explicit is.

Here є means there is / there exists.

This is different from the missing is in тротуар мокрий. In the second clause, the sentence is not just describing калюжа; it is saying that a puddle exists in that place.

So:

• біля світлофора є велика калюжа = there is a big puddle near the traffic light

A useful contrast:

• Тротуар мокрий. = The sidewalk is wet.
• Біля світлофора є калюжа. = There is a puddle near the traffic light.

So є is often used in existential sentences: sentences meaning there is / there are.

Because біля also requires the genitive case.

The noun світлофор changes like this:

• світлофор = traffic light
• біля світлофора = near the traffic light

So again, the pattern is:

• біля + genitive

Other examples:

• біля будинку = near the house
• біля школи = near the school

Because adjectives in Ukrainian must agree with the noun they describe in gender, number, and case.

Here:

1. тротуар is masculine singular nominative, so the adjective is мокрий

   • мокрий тротуар = wet sidewalk
   • тротуар мокрий = the sidewalk is wet

2. калюжа is feminine singular nominative, so the adjective is велика

   • велика калюжа = a big puddle

So:

• masculine noun -> мокрий
• feminine noun -> велика

Because here мокрий is part of the predicate, not just an adjective inside a noun phrase.

There is a difference between:

• мокрий тротуар = a wet sidewalk
• тротуар мокрий = the sidewalk is wet

In your sentence, the meaning is the second one: it is making a statement about the sidewalk.

So the word order helps show that this is a full clause:

• тротуар мокрий = the sidewalk is wet

Yes, Ukrainian word order is fairly flexible, though some orders sound more natural in neutral speech.

This sentence uses a very natural order:

• Після дощу — time/background first
• тротуар мокрий — first statement
• і біля світлофора є велика калюжа — second statement with location first

Why put біля світлофора early? Because Ukrainian often places the location before є in existential sentences:

• На столі є книжка. = There is a book on the table.
• Біля світлофора є велика калюжа. = There is a big puddle near the traffic light.

You may see other word orders, but this one is very standard.

Because і is joining two full clauses, not just two words.

The two clauses are:

1. тротуар мокрий
2. біля світлофора є велика калюжа

Since each part has its own grammatical structure, Ukrainian normally puts a comma before і here.

So the comma is not random; it marks the boundary between two complete ideas.

Usually it means a big puddle here.

Ukrainian has no articles like a and the, so the same phrase can sometimes be translated either way depending on context.

• велика kalюжа = big puddle / a big puddle / the big puddle

In this sentence, because the puddle is being introduced for the first time, English naturally uses a big puddle:

• біля світлофора є велика калюжа = there is a big puddle near the traffic light

Both are in the nominative singular here.

• тротуар is the subject of the first clause
• калюжа is the noun that exists in the second clause, and in this kind of affirmative existential sentence it is also normally in the nominative

So:

• тротуар мокрий
• є велика калюжа

Both nouns appear in their basic dictionary form here.

Sometimes in colloquial Ukrainian, є can be omitted, especially in casual speech, but for learners є is the clearest and safest choice in existential sentences.

So:

• біля світлофора є велика калюжа = very clear, standard there is a big puddle near the traffic light

You may also hear shorter versions in context, but using є is a good habit when you want to say there is / there are.

Світлофор means traffic light.

It is a standard everyday word in Ukrainian. In this sentence:

• біля світлофора = near the traffic light

So the whole second clause tells you where the puddle is located.