J’écris à la bibliothécaire afin qu’elle mette le livre de côté pour Marie.

Because je drops its final e before a vowel sound. This is called elision.

So:

• je écris → j’écris
• je aime → j’aime
• je habite → j’habite

It is done for smoother pronunciation.

In French, écrire à quelqu’un means to write to someone.

So:

• J’écris à la bibliothécaire = I’m writing to the librarian

This is different from:

• écrire quelque chose = to write something
• écrire à quelqu’un = to write to someone

In this sentence, both ideas appear:

• J’écris à la bibliothécaire = I write to the librarian
• le livre is the thing being discussed later in the sentence

Bibliothécaire means librarian.

Here it is la bibliothécaire because the sentence is referring to a female librarian. The later part qu’elle confirms that the librarian is female.

Useful comparison:

• le bibliothécaire = the male librarian
• la bibliothécaire = the female librarian

The noun form itself stays the same; only the article changes.

Afin que means so that or in order that. It introduces a purpose.

So:

• J’écris à la bibliothécaire afin que...
  = I’m writing to the librarian so that...

It is a bit more formal than pour que, though both are common.

Compare:

• afin que = so that, in order that
• pour que = so that

In many contexts, they mean basically the same thing.

This is another case of elision.

When que comes before a word beginning with a vowel sound, it becomes qu’:

• que elle → qu’elle
• que il → qu’il
• que on → qu’on

So afin qu’elle is simply the correct shortened form of afin que elle.

Because afin que requires the subjunctive, and mette is the subjunctive form of mettre for elle.

Here is the contrast:

• Indicative present: elle met = she puts
• Subjunctive present: qu’elle mette

After expressions of purpose like afin que or pour que, French normally uses the subjunctive:

• afin qu’elle mette le livre de côté

This is one of the most important reasons learners meet the subjunctive in everyday French.

The present subjunctive of mettre is:

• que je mette
• que tu mettes
• qu’il/elle mette
• que nous mettions
• que vous mettiez
• qu’ils/elles mettent

So in this sentence, since the subject is elle, the form is mette.

A quick way to recognize it is that after afin que, you expect a subjunctive form, and elle mette matches that pattern.

Literally, mettre ... de côté means to put ... to the side.

But in a library context, it means something more natural in English, such as:

• to set the book aside
• to hold the book
• to reserve the book

So the phrase is somewhat idiomatic here. It does not necessarily mean physically placing it off to one side; it means keeping it available for someone.

Le livre means the book, while un livre means a book.

Using le livre suggests that the speaker and listener already know which book is meant, or that it has already been identified in context.

Compare:

• mettre le livre de côté = set aside the book
• mettre un livre de côté = set aside a book

So le points to a specific book.

Pour Marie means for Marie.

It shows who the book is being set aside for. In other words, Marie is the beneficiary of the action.

• mettre le livre de côté pour Marie = set the book aside for Marie

This is more natural here than à Marie, because the idea is not giving the book directly to Marie at that moment, but reserving it on her behalf.

French present tense often covers both simple present and present progressive meanings in English.

So J’écris can mean:

• I write
• I am writing

Which one sounds best depends on context. In this sentence, English would often naturally say:

• I’m writing to the librarian...

even though French just uses the simple present j’écris.

Yes. You could say:

• J’écris à la bibliothécaire pour qu’elle mette le livre de côté pour Marie.

This has nearly the same meaning: I’m writing to the librarian so that she sets the book aside for Marie.

The main difference is style:

• afin que = a bit more formal
• pour que = very common, slightly more everyday

Both still require the subjunctive.

The sentence breaks down like this:

• J’écris à la bibliothécaire = main clause
• afin qu’elle mette le livre de côté pour Marie = purpose clause

More literally:

• I write to the librarian
• so that she may set the book aside for Marie

So the pattern is:

main action + purpose

That is why the sentence uses afin que followed by the subjunctive.