Första kapitlet var så bra att jag genast skrev upp bokens titel.

Both are possible.

• det första kapitlet is the full, very common definite form.
• första kapitlet without det is also idiomatic, especially with ordinals like första, andra, sista.

The version without det can sound a bit leaner or slightly more literary. So the sentence is natural as written, but Det första kapitlet var så bra ... would also be correct.

Because kapitel is an ett noun, and here it is in the definite singular form:

• ett kapitel = a chapter
• kapitlet = the chapter

So första kapitlet means the first chapter.

This is a spelling pattern in Swedish. Many words ending in -el, -en, or -er lose an unstressed vowel in some forms.

So:

• kapitel + et becomes kapitlet

This is normal and must mostly just be learned as part of the noun’s forms.

It is the common pattern:

så + adjective/adverb + att = so ... that

So:

• så bra att = so good that

In the sentence, it connects the first idea to the result:

• the first chapter was so good
• that I immediately wrote down the title

Because bra does not change form for gender or number in normal use.

For example:

• en bok är bra
• ett kapitel är bra
• böcker är bra

So even though kapitlet is neuter, the adjective is still simply bra.

Var is the past tense of är from the verb vara = to be.

So:

• är = is / are
• var = was / were

Here kapitlet var så bra means the chapter was so good.

Genast means immediately, at once, or right away.

It shows that the action happened very quickly after reading the chapter. Compared with direkt, genast can sound a little more formal or written, but both are common.

Skrev upp is the past tense of the particle verb skriva upp, which means to write down or to note down.

• skriva upp = to write down
• skrev upp = wrote down

In Swedish, particle verbs often split when the verb is finite:

• Jag skrev upp titeln.
• Jag vill skriva upp titeln.

So upp is separate here because skrev is a finite past-tense verb.

Because in Swedish, a possessor usually replaces the article on the thing possessed.

So:

• bokens titel = the book’s title
• not bokens titeln

The same pattern appears in:

• min bil = my car
• Peters hus = Peter’s house

Even though titel is not marked with the definite ending, the whole phrase is definite because of bokens.

Yes. Both are natural:

• bokens titel
• titeln på boken

They mean essentially the same thing. Very roughly:

• bokens titel can sound a bit more compact or written
• titeln på boken can sound a bit more explicit or conversational

Here att means that. It introduces the result clause after så bra.

So:

• så bra att jag genast skrev upp bokens titel
• so good that I immediately wrote down the book’s title

This att is not the infinitive marker seen in phrases like att läsa.

Because after att, Swedish uses subordinate clause word order.

That means the subject jag stays before the finite verb:

• ... att jag genast skrev upp bokens titel

In a main clause, Swedish normally has verb-second word order, but after att you do not get that same pattern. The clause structure here is therefore completely normal.

Because the sentence describes a completed situation in the past:

• var = was
• skrev upp = wrote down

Swedish often uses the simple past in exactly the same kind of context where English uses was and wrote down.