U knjižnici često održavaju večernja čitanja, a baka poslije toga uvijek spominje svoje omiljene pjesnike.

Because u means in here, and when it expresses location, Croatian normally uses the locative case.

• dictionary form: knjižnica = library
• locative singular: knjižnici

So:

• u knjižnici = in the library

If u meant movement into, you would usually expect the accusative instead.

This is a very common Croatian pattern. Održavaju is 3rd person plural, literally they hold / they organize, but the subject is left unspecified.

In English, we often translate this as something like:

• they hold evening readings
• evening readings are often held
• the library often organizes evening readings

So the sentence does not tell us exactly who they are. It just means that this regularly happens.

Here održavaju means they hold, they organize, or they put on.

The verb is održavati in the imperfective form, which fits well with često because it describes a repeated or habitual action:

• često održavaju = they often hold / organize

In other contexts, održavati can also mean things like maintain or keep up, so the exact meaning depends on context.

Večernja čitanja means evening readings or evening reading events.

Breakdown:

• večernji / večernja / večernje = evening
• čitanje = reading
• čitanja = readings

Here čitanja is a neuter plural noun, and the adjective večernja agrees with it in gender, number, and case.

So:

• singular: večernje čitanje = an evening reading
• plural: večernja čitanja = evening readings

Both can mean something like and, but they are not used in exactly the same way.

• i simply adds another piece of information: and
• a often connects two related clauses with a slight contrast, shift, or change of focus

Here:

• U knjižnici često održavaju večernja čitanja, a baka...

This feels like:

• Evening readings are often held in the library, and meanwhile / and as for grandma, she...

So a is very natural because the sentence moves from one idea to another related one.

Poslije toga means after that.

• poslije = after
• toga = that in the genitive case

After poslije, Croatian normally uses the genitive, which is why you get toga, not the basic form to.

A very common alternative is:

• nakon toga = after that

Both are natural.

Uvijek means always, so the sentence is describing a habitual action. Because of that, Croatian uses the imperfective verb spominjati here:

• spominje = mentions, keeps mentioning, talks about

So:

• baka uvijek spominje... = grandma always mentions...

This is not about one single completed mention, but about something she regularly does.

Because svoje is the reflexive possessive and it refers back to the subject of the clause, which here is baka.

So:

• baka spominje svoje omiljene pjesnike = grandma mentions her own favorite poets

Croatian strongly prefers svoj when the possessor is the same as the subject.

Compare:

• Baka spominje svoje omiljene pjesnike. = Grandma mentions her own favorite poets.
• Baka spominje njezine omiljene pjesnike. = Grandma mentions her favorite poets, but this usually sounds like some other woman's favorite poets, not grandma's.

Because pjesnike is the direct object of spominje, so it must be in the accusative plural.

• dictionary form: pjesnik = poet
• nominative plural: pjesnici = poets
• accusative plural: pjesnike

So:

• spominje pjesnike = mentions poets

The adjective also agrees with the noun:

• omiljene pjesnike = favorite poets

The whole phrase is in the accusative plural, because it is the object of spominje.

All parts match:

• svoje = accusative plural
• omiljene = accusative plural
• pjesnike = accusative plural

Croatian adjectives and possessives agree with the noun they describe.

Not completely. Croatian word order is fairly flexible, but the given order sounds natural and neutral.

For example:

• U knjižnici često održavaju večernja čitanja
• Često održavaju večernja čitanja u knjižnici

Both are possible, but the first version puts emphasis first on where it happens.

Likewise:

• baka poslije toga uvijek spominje...
• baka uvijek poslije toga spominje...

Both can work, but the original has a smooth, natural rhythm.

So the word order here is not random, but it is also not as rigid as in English.