У моей собаки мокрая шерсть после дождя.

In Russian, possession is very often expressed with the pattern:

у + possessor (genitive) + possessed thing

So У моей собаки мокрая шерсть literally works like:

• At my dog, there is wet fur
• natural English: My dog has wet fur

Russian often uses this structure instead of a verb like to have.

Because у requires the genitive case.

The dictionary form is:

• моя собака = my dog

But after у, both words change:

• моя → моей
• собака → собаки

So:

• у моей собаки = of / belonging to my dog, or more naturally, my dog has

This is a very common pattern:

• у меня
• у брата
• у моей собаки

It is genitive singular.

Why?

• у takes the genitive
• собака is singular
• моей agrees with собаки in gender, number, and case

So:

• собака → nominative singular
• собаки → genitive singular
• моя → nominative feminine singular
• моей → genitive feminine singular

Because мокрая describes шерсть, and adjectives in Russian must agree with the noun they describe.

Шерсть is:

• feminine
• singular
• nominative here

So the adjective must also be:

• feminine singular nominative

That gives:

• мокрая шерсть = wet fur

Compare:

• мокрый пёс = wet dog
• мокрая шерсть = wet fur
• мокрое полотенце = wet towel

Because шерсть is the grammatical subject of the sentence.

The structure is basically:

• У моей собаки = with my dog / my dog has
• мокрая шерсть = wet fur

So the thing that is wet is шерсть, and that is why it appears in the nominative.

Even though English focuses on my dog, Russian grammar here is centered on fur as the thing being described.

Yes, in a way.

In the present tense, Russian usually omits есть (is / are) in simple statements like this.

So:

• У моей собаки мокрая шерсть literally has no spoken is
• but in English we translate it as My dog’s fur is wet or My dog has wet fur

Russian does this very often:

• Он врач = He is a doctor
• У меня брат = I have a brother
• У моей собаки мокрая шерсть = My dog has wet fur

Because this sentence specifically talks about the dog’s fur/coat, not necessarily the whole dog in a general way.

• У моей собаки мокрая шерсть = My dog’s fur is wet / My dog has wet fur
• Моя собака мокрая = My dog is wet

Both are possible, but they are not exactly the same:

• мокрая шерсть focuses on the coat/fur
• моя собака мокрая focuses on the dog as a whole

Russian often uses шерсть when talking about an animal’s coat.

Because после takes the genitive case.

The noun is:

• дождь = rain

After после, it becomes:

• дождя = of rain / after rain

So:

• после дождя = after the rain / after rain

This is another useful case pattern to remember:

• после урока = after the lesson
• после работы = after work
• после дождя = after rain

Yes. Russian word order is flexible, although the original sentence is very natural.

Original:

• У моей собаки мокрая шерсть после дождя.

You could also say:

• После дождя у моей собаки мокрая шерсть.

Both are correct. The difference is mostly in emphasis:

• У моей собаки... starts with the possessor
• После дождя... starts with the time/context

Russian word order often changes to highlight what is most important or already known in the conversation.

Grammatically, yes, but it sounds less natural here.

In the present tense, есть is usually omitted when you are simply describing something that exists or has a quality.

So the natural version is:

• У моей собаки мокрая шерсть

Using есть would sound more like you are emphasizing existence in a special way, which is not needed here.

Шерсть usually means an animal’s fur, coat, or hair as a mass of hair covering the body.

In this sentence, the most natural English choices are:

• fur
• coat

So:

• У моей собаки мокрая шерсть = My dog’s fur is wet
• or My dog has a wet coat

For animals, шерсть is much more natural than a word meaning human hair.