Après avoir posé le livre sur la table, je le reprends pour le ranger dans mon sac.

Because French uses the past infinitive here: après avoir posé literally means after having put/placed.

This structure shows that one action happened before the main action:

• avoir posé le livre = having placed the book
• je le reprends = I pick it up again

So après + past infinitive is a very common way to say after doing something when the subject is the same in both actions.

French forms the past infinitive with:

• avoir or être in the infinitive
• plus a past participle

Here, the verb is poser, which normally uses avoir in compound tenses:

• j’ai posé
• so the infinitive version becomes avoir posé

If the verb took être, you would get something like après être arrivé.

Because posé is the past participle, and here it does not agree.

With avoir, the past participle usually agrees only if a direct object comes before it. In this sentence:

• avoir posé le livre
• the direct object le livre comes after posé

So the participle stays in the default masculine singular form:

• posé

If a preceding direct object were present, agreement could happen in other contexts.

Reprendre means to take again, to pick up again, or to take back.

So:

• je prends le livre = I take the book
• je reprends le livre = I take the book again / I pick the book back up

In this sentence, the book was placed on the table first, and then taken again, so reprendre is the natural verb.

In French, object pronouns usually come before the conjugated verb.

So instead of:

• je reprends le livre

you can replace le livre with le:

• je le reprends

This le means it, referring to le livre.

That is normal French word order for object pronouns.

That le is also a direct object pronoun, and it still refers to le livre.

The phrase:

• pour le ranger means
• in order to put it away

Here, ranger means to put away / to store / to tidy away.

So the sentence uses le twice because the book is the object of two different verbs:

• je le reprends = I pick it up again
• pour le ranger = to put it away

Because French object pronouns go before the infinitive they belong to.

So:

• ranger le livre = to put away the book
• le ranger = to put it away

After pour, you normally use an infinitive to express purpose:

• pour ranger le livre
• pour le ranger

Both are possible, but once you use the pronoun le, it must come before ranger.

Pour here expresses purpose or intention:

• pour le ranger dans mon sac = in order to put it away in my bag

So the structure is:

• main action: je le reprends
• purpose: pour le ranger dans mon sac

This is very common in French:

• Je viens pour aider.
• Il ouvre la porte pour entrer.

Because après avoir posé does not set the whole sentence in the past. It only shows that the action of placing the book happened before the action of picking it up again.

The main verb can still be in whatever tense fits the context:

• je le reprends = present
• je l’ai repris = past
• je le reprendrai = future

So this sentence could describe:

• a habitual action
• a live narration
• a general sequence of actions

The important point is the relative order:

1. place the book
2. pick it up again
3. put it in the bag

Because sur means on, while dans means in.

A book rests on a table, so French uses:

• sur la table = on the table

You would only use dans if the object were inside something:

• dans le sac = in the bag
• dans la boîte = in the box

Both are grammatically possible, but dans mon sac is more specific: it means in my bag.

French often uses possessive adjectives like:

• mon = my
• ton = your
• son = his/her/its

So:

• dans le sac = in the bag
• dans mon sac = in my bag

The second one tells you exactly whose bag it is.

Yes, it could, but the nuance is slightly different.

• poser = to put down / place
• mettre = to put

Poser often suggests placing something down onto a surface, so it fits very naturally with sur la table.

So:

• poser le livre sur la table sounds very natural
• mettre le livre sur la table is also correct, but a little more general

Not exactly.

• mettre dans mon sac = put into my bag
• ranger dans mon sac = put away into my bag / store in my bag

Ranger often adds the idea of putting something in its proper place, tidying it away, or storing it neatly.

So in this sentence, ranger suggests more than just movement; it suggests putting the book away properly.

It has three parts:

1. Après avoir posé le livre sur la table

   • a time clause meaning after placing the book on the table

2. je le reprends

   • the main clause: I pick it up again

3. pour le ranger dans mon sac

   • a purpose clause: to put it away in my bag

So the sentence is built like this:

After having placed the book on the table, I pick it up again to put it away in my bag.

This kind of structure is very common in French:

• time expression
  • main action
    • purpose