Learn Hardcore Portuguese (Portugal): Os livros deles estão na estante.

Os livros literally means the books.
In a neutral statement about specific books that both speakers know about, Portuguese almost always uses the article.

If you said just Livros deles estão na estante, it would sound odd and incomplete, like saying “Books of theirs are on the shelf” with something missing. In most normal contexts you want os livros here.

What does deles literally mean, and how is it formed?

Deles is a possessive form meaning of them / their / theirs (when “they” are male or a mixed group).

It’s formed from:

de (of) + eles (they / them) → deles = of them

Other similar forms are:

dele = of him / his
dela = of her / hers
deles = of them / their / theirs (masculine or mixed group)
delas = of them / their / theirs (all-female group)

You don’t normally say de eles separately; you use the fused form deles.

What’s the difference between os livros deles and os seus livros?

Both can be translated as their books, but there’s an important difference in clarity:

os livros deles = their books (clearly refers to they/them mentioned in the context)
os seus livros can mean:
- your books (formal you, singular or plural), or
- his books, her books, their books

So seus is ambiguous. In European Portuguese, people often prefer dele / dela / deles / delas (after the noun) to avoid confusion:

os livros deles = clearly their books (of those people we’re talking about)
os seus livros could be misunderstood as your books (polite “you”).

That’s why os livros deles is a very natural, unambiguous choice.

Why is the possessive after the noun (os livros deles) instead of before, like English “their books”?

Portuguese allows both positions:

os seus livros (possessive before)
os livros deles (possessive after)

In European Portuguese:

Possessive before the noun (os seus livros) sounds a bit more formal or written, and, as mentioned, can be ambiguous.
Possessive with dele / dela / deles / delas after the noun (os livros deles) is very common in speech and is clearer about whose books they are.

So os livros deles is natural, clear, and stylistically neutral.

How do I choose between deles and delas?

You choose based on the gender of the owners, not the objects:

deles = of them (a group that is all male or mixed male/female)
- Os livros deles = their books (belonging to João and Pedro; or João and Maria)
delas = of them (a group that is all female)
- Os livros delas = their books (belonging to Ana and Maria)

The noun livros is masculine, but that does not affect the choice between deles and delas. Only the people who own the books matter.

Why is it estão and not está or são?

There are two separate issues: plural and which verb.

Plural agreement
- Subject: Os livros (plural)
- Verb: must be plural → estão (they are)
- está is singular (“is” for one thing).
Estar vs. ser
- estar is used here for location (where something is):
  - Os livros estão na estante. = The books are on the shelf.
- ser (são) is used for more permanent characteristics, identity, etc.:
  - Os livros são caros. = The books are expensive.

So for where the books are, you need estar in the plural: estão.

What exactly is na in na estante? Why not just em a estante?

Na is a mandatory contraction of the preposition em (in / on / at) and the feminine singular article a (the):

em + a → na

Similarly:

em + o → no
em + as → nas
em + os → nos

In standard Portuguese, you almost never say em a estante; you must contract it to na estante. So na estante literally is in/on the shelf.

Does na estante mean “in the shelf” or “on the shelf”? Why not use sobre?

In Portuguese, em (and therefore na) is very flexible and is used for both in and on, depending on context:

Os livros estão na estante.
→ The books are on the shelf (or on the bookcase shelves).

You could say sobre a estante but that usually suggests “on top of the shelf/bookcase” (maybe on the very upper surface, not on the shelves where books normally go).

So:

na estante = in its normal place, on the shelves / in the bookcase
sobre a estante = on the upper surface, maybe on top of the furniture

Why is it a estante (feminine) and how does that affect the rest of the sentence?

Nouns in Portuguese have grammatical gender. Estante (shelf / bookcase) is feminine, so it takes the feminine singular article a:

a estante = the shelf/bookcase

This gender affects:

The article: a (not o)
Contractions: em + a → na estante

It does not affect the gender of livros, which is its own word (masculine plural → os livros). So you get a mix:

Os livros (masc. pl.)
na estante (fem. sg.)

Can I omit anything here, like the article os or deles, and still be correct?

You can change or omit some elements, but the meaning changes:

Os livros estão na estante.
→ The books are on the shelf. (no owner mentioned)
Livros deles estão na estante.
This is grammatically possible but feels unusual/marked; Portuguese really wants the article here.
Os livros na estante.
Without a verb, this is not a complete sentence; it’s just a noun phrase (“The books on the shelf”).

To keep the same meaning as the original — Their books are on the shelf — you really need all the parts:

Os livros deles estão na estante.

How would the sentence change if there were only one book, or if it belonged to just one person?

One book, same (plural) owners
- O livro deles está na estante.
  → Their book is on the shelf.
  Changes:
- livro (singular), so o livro
- Verb agrees in singular: está
Many books, one male owner
- Os livros dele estão na estante.
  → His books are on the shelf.
Many books, one female owner
- Os livros dela estão na estante.
  → Her books are on the shelf.
One book, one male owner
- O livro dele está na estante.
One book, one female owner
- O livro dela está na estante.

Is this sentence the same in Brazil, or would Brazilians say it differently?

The sentence Os livros deles estão na estante. is completely correct and natural both in Portugal and in Brazil.

Differences:

Pronunciation will be different (European vs. Brazilian accent).
In Brazil, people might also often say Os livros deles estão na estante with identical words and word order.
Both varieties also have Os seus livros estão na estante, with the same potential ambiguity.

So in terms of grammar and vocabulary, it’s shared by both European and Brazilian Portuguese.