У оленя красивые рога, но коза подошла к нам ближе и совсем не боялась.

Russian very often expresses possession with the pattern:

у + possessor in the genitive + есть / implied there is

So У оленя красивые рога literally feels like:

At the deer, there are beautiful antlers.

This is the normal, natural way to say the deer has beautiful antlers.

A few key points:

• у = by / at
• оленя is the genitive singular of олень
• In the present tense, есть is often omitted when it is just giving simple existence/possession

So:

• У оленя красивые рога. = The deer has beautiful antlers.
• More literally: The deer has, by it, beautiful antlers.

Using иметь is possible in Russian, but it is often less natural in everyday speech for ordinary possession.

Because у requires the genitive case.

The dictionary form is:

• олень = deer

After у, it changes to:

• у оленя = of the deer / by the deer

This is a very common pattern:

• у брата = with the brother / the brother has
• у сестры = with the sister / the sister has
• у меня = I have

So оленя is not a different word; it is just the genitive form of олень.

Because it agrees with рога, which is plural.

In Russian, adjectives must agree with the noun in:

• gender
• number
• case

Here:

• рога = antlers / horns (plural)
• so the adjective must also be plural:
• красивые = beautiful (plural)

So:

• красивый рог = a beautiful horn
• красивые рога = beautiful horns / antlers

Yes. Рога is the normal plural form of рог.

• рог = horn
• рога = horns / antlers

For a deer, Russian commonly uses рога even though English often specifically says antlers. Russian does not always make the same horn/antler distinction as English does in everyday usage.

So У оленя красивые рога is a natural way to say that the deer has beautiful antlers.

Because коза is a feminine singular noun, and past-tense verbs in Russian agree with the subject in gender and number.

The verb is подойти = to approach / come up.
Past tense forms:

• подошёл = masculine
• подошла = feminine
• подошло = neuter
• подошли = plural

Since коза is feminine:

• коза подошла = the goat approached

This gender agreement is a very important feature of Russian past tense.

Подошла is the feminine past form of подойти, which usually means:

• to come up to
• to approach
• to move closer to

So in this sentence, коза подошла к нам ближе means the goat moved nearer to us.

A useful contrast:

• шла = was walking
• подошла = came up / approached

The prefix под- often adds the idea of moving up to something.

К takes the dative case, and нам is the dative form of мы (we).

Pronoun forms:

• мы = we
• нас = us (genitive/accusative, in some uses)
• нам = to us

So:

• к нам = to us / toward us

Examples:

• Он подошёл к нам. = He came up to us.
• Она позвонила нам. = She called us.

So in your sentence:

• коза подошла к нам = the goat came up to us

Ближе is the comparative form meaning closer.

It comes from:

• близко = close, near (as an adverb)
• ближе = closer

Russian often uses special comparative forms rather than a separate word meaning more.

Examples:

• быстро → быстрее = fast → faster
• далеко → дальше = far → farther
• близко → ближе = close → closer

So:

• подошла ближе = came closer

This is completely natural Russian.

Good question. Yes, подошла already contains the idea of approaching, so ближе adds extra emphasis or precision.

Compare:

• коза подошла к нам = the goat came up to us
• коза подошла к нам ближе = the goat came closer to us / came nearer to us

So ближе is not strictly necessary, but it makes the image clearer: the goat reduced the distance even more.

English does this too:

• She came up to us.
• She came closer to us.

Совсем adds emphasis. Here it means something like:

• not at all
• completely not
• really not

So:

• не боялась = was not afraid
• совсем не боялась = was not afraid at all

This makes the statement stronger.

Examples:

• Я совсем не устал. = I’m not tired at all.
• Он совсем не понял. = He didn’t understand at all.

In your sentence, it shows that the goat was very calm and fearless.

In Russian, бояться can be used either:

1. with an object
2. without one, when the meaning is general

So both are possible:

• Коза не боялась. = The goat wasn’t afraid.
• Коза не боялась нас. = The goat wasn’t afraid of us.

When the object is obvious from context, Russian often leaves it out. Here, since the goat came closer to us, it is easy to understand that it was not afraid in general, and probably not afraid of us.

For the same reason as подошла: Russian past-tense verbs agree with the subject.

The subject is коза, which is feminine singular, so the verb must also be feminine singular:

• коза боялась = the goat was afraid
• коза не боялась = the goat was not afraid

Compare:

• козёл боялся = the male goat was afraid
• козы боялись = the goats were afraid

Боялась comes from the imperfective verb бояться.

The imperfective is used here because it describes a state rather than a single completed action. Being afraid is not usually treated as a one-time completed event; it is an ongoing condition.

So:

• не боялась = was not afraid

This fits the context well: the sentence is describing how the goat behaved.

Yes, Russian word order is fairly flexible, but the given order is natural and clear.

Current order:

• но = but
• коза = the goat
• подошла к нам ближе = came closer to us
• и совсем не боялась = and was not afraid at all

This gives a smooth narrative progression:

1. contrast with the deer: но
2. new subject: коза
3. action: подошла
4. extra detail: ближе
5. second description: совсем не боялась

You could move things for emphasis, for example:

• Но ближе к нам подошла коза...
• Но коза совсем не боялась и подошла к нам ближе.

These are possible, but they change the emphasis. The original sentence is the most straightforward.

In the present tense, Russian often omits есть when it simply means there is / there are in a basic statement of possession or existence.

So:

• У оленя красивые рога. = The deer has beautiful antlers.

You could think of an underlying structure like:

• У оленя есть красивые рога.

But in many contexts, especially when simply describing something, Russian leaves есть out.

A rough tendency:

• У меня есть книга. = I have a book.
  This often emphasizes that I possess one.
• У меня новая книга. = I have a new book.
  This is more descriptive.

In your sentence, the speaker is describing the deer’s antlers, so omitting есть is very natural.