У козы маленькие рога, а у оленя рога намного больше.

This is a very common Russian way to express possession.

Russian often says:

у + genitive + [something possessed]

Literally, у козы маленькие рога is something like At the goat, small horns or The goat has small horns.

So:

• у козы = the goat has / at the goat
• у оленя = the deer has / at the deer

Russian does not usually use a direct equivalent of English have in simple possession sentences like this.

Because after у, the noun goes into the genitive case.

Here:

• коза → козы
• олень → оленя

So:

• у козы = of the goat / at the goat
• у оленя = of the deer / at the deer

This is just the normal case pattern required by у in this kind of possession structure.

Because the sentence is talking about horns/antlers as a pair, so Russian uses the plural.

• рог = horn
• рога = horns

Since goats and deer normally have two horns/antlers, the plural is the natural choice here.

Because adjectives must agree with the noun they describe.

Here the noun is рога, which is plural, so the adjective also has to be plural:

• маленький = masculine singular
• маленькая = feminine singular
• маленькое = neuter singular
• маленькие = plural

So:

• маленькие рога = small horns

It is nominative plural.

In this sentence, рога is the thing being described as existing/being a certain way:

• У козы маленькие рога
• У оленя рога намного больше

So рога is not an object here. It is the noun being talked about, which is why it stays in the nominative.

Because in the present tense, Russian usually leaves out to be.

So Russian often says:

• Он врач = He is a doctor
• У козы маленькие рога = The goat has small horns
• Рога намного больше = The horns are much bigger

English needs is/are/has, but Russian often does not.

Here а means something like whereas, while, or and on the other hand.

The sentence compares two animals:

• У козы маленькие рога, а у оленя...

So а introduces a contrast, but not a strong contradiction.

Compare:

• а = contrast between two things
• но = stronger but, often showing something unexpected

In this sentence, а is the natural choice because the speaker is simply setting one fact against another.

Because больше is a comparative form: bigger / larger.

• большие рога = big horns
• рога больше = the horns are bigger

The sentence is not just saying the deer's horns are big. It is saying they are bigger than the goat's horns.

Also, Russian comparatives like больше do not change for gender, number, or case here. They stay the same.

Намного means much, far, or by a lot.

So:

• больше = bigger
• намного больше = much bigger / far bigger

It strengthens the comparison.

You can think of it as adding emphasis:

• not just bigger
• but a lot bigger

It is repeated for clarity and balance.

The full structure is:

• У козы маленькие рога
• а у оленя рога намного больше

Repeating рога makes the comparison very clear and sounds natural.

Russian can sometimes omit repeated words if the meaning is obvious, but in a simple textbook-style sentence, repeating the noun is normal and helpful.

Yes. In Russian, рога is the normal everyday word used for both horns and antlers in many contexts.

So:

• goat horns = рога
• deer antlers = also рога

English makes a stronger everyday distinction between horns and antlers than Russian does.

The word order is natural, but Russian word order is more flexible than English word order.

Starting with у козы and у оленя puts the focus first on whose horns we are talking about. That works well because the sentence is comparing two animals.

So the structure is basically:

• as for the goat...
• and as for the deer...

Other word orders are possible, but this one is very natural for a comparison.