Holnap korán el fogok indulni a könyvtárba.

Hungarian often forms the future with the auxiliary verb fog plus an infinitive.

• fogok = I will
• indulni = to leave / to set off

So:

• el fogok indulni = I will set off / I’m going to leave

This is one of the standard ways to talk about the future in Hungarian.

A very literal breakdown is:

• fogok = I will
• elindulni = to set off

So the whole verbal idea is I will set off.

The ending -ni is the infinitive ending in Hungarian, like to + verb in English.

Examples:

• indulni = to leave / to set off
• menni = to go
• olvasni = to read

In this sentence, indulni is the infinitive used after fogok.

El is a verbal prefix (also called a preverbal particle). With many Hungarian verbs, this prefix normally attaches to the verb:

• elindul = set off / start leaving

But when a finite auxiliary like fogok appears, the prefix is often placed before the auxiliary instead of directly on the infinitive:

• el fogok indulni

So even though the dictionary-style verb is elindul, in this future structure it gets split up.

This is very normal in Hungarian.

Compare:

• Elindulok. = I’m leaving / I set off.
• El fogok indulni. = I will leave / I will set off.

Indulni means to leave, to start, to depart.

With the prefix el-, the meaning becomes more clearly to set off / to depart / to get going.

So:

• indulni = to start leaving / to depart
• elindulni = to set off, to actually head out

In many contexts, elindulni sounds more complete or goal-directed than plain indulni.

In this sentence, el fogok indulni suggests I’ll set off rather than just I’ll be starting.

Because fog here is being used as an auxiliary, and it takes the indefinite conjugation.

• fogok = I will
• fogom would be a definite form, used when fog means I am holding/catching it or when it takes a definite object.

For example:

• Fogok indulni. = I will leave.
• Fogom a könyvet. = I’m holding the book.

So in your sentence, fogok is correct because it is part of the future construction, not the main lexical verb to hold.

The ending -ba means into or to ... inside.

• könyvtár = library
• könyvtárba = into the library / to the library

So a könyvtárba means to the library.

Hungarian often distinguishes direction very clearly:

• -ba / -be = into
• -ban / -ben = in
• -ból / -ből = out of

Examples:

• a könyvtárba = to the library
• a könyvtárban = in the library
• a könyvtárból = out of the library

Yes, Hungarian often uses the definite article where English may or may not use the.

• a könyvtárba = to the library

This is the most natural form if the speaker has a specific library in mind, or if the place is understood from context.

Without the article:

• könyvtárba

this can also occur, but it often sounds more general or appears in certain set expressions and stylistic contexts.

For a learner, a könyvtárba is the safest and most natural choice in a normal sentence like this one.

Hungarian word order is flexible, and the beginning of the sentence often gives the topic or the element the speaker wants to set up first.

Starting with Holnap puts the time frame first:

• Holnap = tomorrow

So the sentence first tells you when, and then gives the rest of the information.

This is very natural in Hungarian.

You could rearrange the sentence in other ways, but Holnap korán el fogok indulni... is a very normal neutral order.

Korán is an adverb meaning early.

In this sentence:

• Holnap korán el fogok indulni...

it comes after the time word holnap and before the verb phrase. This is a common, natural position for adverbs in a neutral sentence.

The order feels like:

• Tomorrow
• early
• I will set off
• to the library

So Hungarian is organizing the sentence from time information toward the action.

Yes, very often.

Hungarian frequently uses the present tense to talk about future events when the time is already clear from context.

For example:

• Holnap korán elindulok a könyvtárba.

This can also mean Tomorrow I’m leaving early for the library or Tomorrow I leave early for the library.

The version with fogok makes the future meaning more explicit:

• Holnap korán el fogok indulni a könyvtárba.

Both are correct, but the present-tense version is often very common in everyday Hungarian.

It is the normal neutral order for this structure, but Hungarian word order can change for emphasis.

The basic idea is that the verbal prefix el is separated because of fogok:

• el fogok indulni

That is the standard form here.

Other word orders are possible in special contexts, especially if you want to emphasize a particular word, but for a learner this is the pattern to remember.

So the safest model is:

• prefix + fog + personal ending + infinitive

Example:

• el fogok indulni
• meg fogom nézni
• be fogunk menni

The ending -ok in fogok marks first person singular: I.

So:

• fogok = I will
• fogsz = you will
• fog = he/she/it will
• fogunk = we will
• fogtok = you (plural) will
• fognak = they will

In your sentence, fogok shows that the subject is I, so Hungarian does not need a separate word for I unless you want emphasis.

That is why the sentence does not need én.

Hungarian usually leaves out subject pronouns when the verb ending already shows the subject.

Here:

• fogok already means I will

So én is unnecessary unless you want emphasis or contrast.

Compare:

• Holnap korán el fogok indulni a könyvtárba. = neutral
• Én holnap korán el fogok indulni a könyvtárba. = I will leave early tomorrow (perhaps contrasting with someone else)

So omitting én is the normal choice.