Post scholam liber magistro dandus est.

Because post is a preposition that takes the accusative.

So:

• post = after
• schola = school
• post scholam = after school

This is true whether post is being used in a spatial sense (behind) or a temporal sense (after).

Liber is nominative singular, so it is the subject of the sentence.

In this sentence, the basic structure is:

• liber = the book
• dandus est = must be given / is to be given

So literally the sentence is something like:

The book is to be given to the teacher after school.

Even though English often says someone must give the book, Latin here is built around the book as the grammatical subject.

Dandus est is a gerundive + form of esse, often called the passive periphrastic.

It expresses necessity or obligation.

So:

• dandus = to be given / needing to be given
• est = is

Together:

• dandus est = must be given / has to be given / is to be given

So liber magistro dandus est means:

The book must be given to the teacher.

This is a very common Latin way to express must.

Because dandus agrees with liber.

The gerundive works like an adjective, so it must match the noun it describes in:

• gender
• number
• case

Here:

• liber is masculine
• singular
• nominative

So the gerundive must also be:

• masculine
• singular
• nominative

That gives dandus.

If the subject were feminine singular, you would get danda est.
If it were neuter singular, dandum est.

Because magistro is the person to whom the book is given.

The dative case often shows the indirect object:

• magister = teacher
• magistro = to/for the teacher

So:

• liber magistro dandus est = the book must be given to the teacher

Latin usually does not need a separate word for to here, because the dative ending already shows that meaning.

No. Here magistro is the recipient, not the agent.

It means:

• to the teacher

not:

• by the teacher

If Latin wants to express the personal agent with an ordinary passive verb, it often uses ab + ablative, for example ab magistro = by the teacher.

However, with the passive periphrastic, the person who has the obligation can sometimes appear in the dative too. But in this sentence, the most natural reading is that magistro is the person receiving the book.

Because Latin often expresses must through grammar rather than with a separate word.

In English:

• The book must be given

In Latin:

• liber dandus est

So the sense of obligation is built into the combination of:

• the gerundive (dandus)
• plus esse (est)

This is one of the standard Latin ways to say that something has to be done.

Latin word order is much more flexible than English word order because the endings show each word’s job in the sentence.

So Latin can say:

• Post scholam liber magistro dandus est

instead of a more English-like order such as:

• Liber post scholam magistro dandus est

or even:

• Liber magistro post scholam dandus est

All of these can mean essentially the same thing.

The chosen order may reflect emphasis or style. Starting with Post scholam puts the time phrase first, a bit like saying After school, the book must be given to the teacher.

Classical Latin does not have definite or indefinite articles like English the or a/an.

So:

• liber can mean a book or the book
• magistro can mean to a teacher or to the teacher
• scholam can mean school or the school, depending on context

The exact English translation depends on the situation. Latin leaves that to context.

Grammatically, it is simply after school or after the school/session, depending on context.

Because Latin has no article, scholam by itself does not tell you whether English should use the. Also, schola can refer not only to the physical school but also to school time, class, or a lesson, depending on context.

So post scholam is a normal way to express a time idea like after school.

It comes from do, dare, dedi, datus, which means to give.

The gerundive is formed from the verb stem, so from dare we get:

• dandus, danda, dandum = to be given / needing to be given

So in this sentence:

• dandus est = is to be given / must be given

Knowing the principal parts helps you recognize that dandus belongs to the verb to give.