En el mercado vuelve a haber mucha gente.

Volver a + infinitive means to do something again.

So:

• vuelve a haber = there is / there are again
• literally, something like it returns to there being

This is a very common structure in Spanish:

• Volví a leer el mensaje. = I read the message again.
• Vamos a verlo otra vez and vamos a volver a verlo are both possible, but volver a + infinitive is a very standard way to say again.

In your sentence, vuelve a haber mucha gente means that the market had stopped being crowded, and now it is crowded again.

That a is required by the structure volver a + infinitive.

So:

• volver a comer = to eat again
• volver a intentarlo = to try again
• volver a haber = to be again / to exist again

You cannot normally leave that a out.
So vuelve haber would be incorrect.

Actually, hay comes from haber.

• haber = the infinitive
• hay = the present-tense impersonal form, meaning there is / there are

After volver a, Spanish needs an infinitive, not a conjugated form. That is why you get:

• vuelve a haber mucha gente

and not:

• vuelve a hay mucha gente ✘

Compare:

• Hay mucha gente. = There are a lot of people.
• Vuelve a haber mucha gente. = There are a lot of people again.

Spanish uses haber in impersonal expressions meaning there is / there are.

So to say that people are present somewhere, Spanish normally says:

• Hay mucha gente en el mercado.

not:

• Está mucha gente en el mercado. ✘
• Es mucha gente en el mercado. ✘

Why?

• haber introduces the existence or presence of something: there is / there are
• estar describes the location or state of something specific
• ser is not used for this idea

You could use estar if you are talking about specific people:

• Mis amigos están en el mercado. = My friends are at the market.

But for there are a lot of people, Spanish uses haber.

Gente is usually a singular collective noun meaning people in a general sense.

So Spanish says:

• mucha gente = a lot of people

not usually:

• muchas gentes

Even though the meaning is plural in English, grammatically gente is singular in Spanish.

That is why you say:

• Hay mucha gente.
• La gente está cansada.

not:

• La gente están cansados. ✘

The form gentes does exist, but it is much less common and usually has a more special meaning, such as peoples, groups of people, or different kinds of people.

Grammatically, gente is singular.

That affects articles, adjectives, and verbs connected to it:

• mucha gente
• la gente
• la gente está...

So you would say:

• Hay mucha gente en el mercado.
• La gente es amable.
• La gente está contenta.

Notice that adjectives often agree in the singular too:

• La gente está cansada.

In everyday speech, some speakers may sometimes mix singular and plural ideas because the meaning is plural, but for learners, the safe and standard rule is:

• treat gente as singular

Spanish is flexible with word order, and starting with the place is very common.

• En el mercado vuelve a haber mucha gente.
• Vuelve a haber mucha gente en el mercado.

Both are correct.

Starting with En el mercado helps set the scene first, a bit like:

• At the market, there are a lot of people again.

This kind of fronting is very natural in Spanish, especially when the speaker wants to focus first on the location.

Because en expresses location: in / at the market.

• en el mercado = in/at the market

But a or al usually expresses movement toward somewhere:

• Voy al mercado. = I’m going to the market.

In your sentence, the market is the place where the people are, not the destination of movement. So en is the correct preposition.

Yes, often you can.

For example:

• En el mercado hay otra vez mucha gente.
• En el mercado vuelve a haber mucha gente.

Both can mean roughly the same thing.

However, volver a + infinitive is often a bit more idiomatic when talking about something happening again. It can sound slightly more integrated and natural than just adding otra vez.

A small nuance:

• volver a + infinitive focuses on the repetition of the action/state
• otra vez simply adds again

So in many contexts they are interchangeable, but vuelve a haber is a very natural choice here.

Because with this structure, the verb is not agreeing with gente as a subject.

In hay mucha gente, Spanish uses haber impersonally. That means:

• there is no true grammatical subject
• mucha gente is the thing whose existence is being stated

So Spanish says:

• hay mucha gente
• había mucha gente
• hubo mucha gente

not:

• hayan mucha gente ✘
• habían mucha gente ✘ in standard Spanish for this meaning

This is important: with impersonal haber, the verb stays singular.

Vuelve is the third person singular present tense of volver.

• yo vuelvo
• tú vuelves
• él/ella/usted vuelve

It is conjugated because it is the main verb of the sentence pattern volver a + infinitive.

The second verb, haber, stays in the infinitive because it depends on volver a:

• vuelve a haber
• volvió a haber
• va a volver a haber

So the tense is carried by volver, while haber remains unchanged as an infinitive.

In English, you would normally translate it as there are a lot of people again, because people is plural.

But in Spanish, the equivalent structure uses singular impersonal haber:

• hay mucha gente
• vuelve a haber mucha gente

So even though English chooses are, Spanish still uses the singular impersonal verb form.

That is one of the places where English and Spanish grammar do not match directly.