Mihi hic liber hodie legendus est.

Because this sentence uses the gerundive of obligation (also called the passive periphrastic), and in that construction the person who has the obligation is usually put in the dative.

So:

• mihi = for me / by me / I have to
• not ego, because ego would be nominative, and here Latin is not making I the grammatical subject

A very literal sense is:

• Mihi hic liber legendus est = This book is to-be-read by me

More natural English is:

• I have to read this book

So mihi is functioning as the dative of agent, which is especially common with this construction.

Legendus est is made of:

• legendus = a gerundive of legere (to read)
• est = is

Together they form a standard Latin expression of necessity or obligation:

• legendus est = must be read, has to be read, or more literally is to be read

This is not just a normal future idea like will be read. It specifically adds a sense of necessity.

So:

• hic liber legendus est = this book must be read

Because in this construction the thing that must be read becomes the grammatical subject of the sentence.

Latin is structuring the idea as:

• The book must be read by me

not as:

• I must read the book

That is why:

• liber is nominative singular
• legendus agrees with it in nominative singular masculine
• est is singular, matching liber

So even though English would often make I the subject, Latin here makes the book the subject.

Because hic has to agree with liber.

Liber is:

• masculine
• singular
• nominative

So the demonstrative must also be:

• masculine
• singular
• nominative

That gives:

• hic liber = this book

Compare:

• hic liber = masculine nominative singular
• hunc librum = masculine accusative singular
• hoc = neuter nominative/accusative singular

Since liber is the subject here, nominative hic is the correct form.

Because the gerundive behaves like an adjective and must agree with the noun it describes.

Here it describes liber, so it matches liber in:

• gender: masculine
• number: singular
• case: nominative

So:

• liber → masculine singular nominative
• legendus → masculine singular nominative

If the noun changed, the gerundive would change too:

• libri legendi sunt = the books must be read
• epistula legenda est = the letter must be read

They are very similar in meaning, but they are not structured the same way.

mihi hic liber hodie legendus est

• literally: this book is to be read by me today
• uses the gerundive of obligation
• focuses on the book as the thing under necessity

ego hunc librum hodie legere debeo

• literally: I ought/must read this book today
• uses debeo
• focuses more directly on I as the subject

Both can often be translated as:

• I have to read this book today

But the gerundive construction is a very characteristic Latin way of expressing obligation, and it often sounds a bit more formal or objective.

Because this is a special kind of passive expression.

In a normal passive sentence, the personal agent is usually expressed with a/ab + ablative:

• Liber a me legitur = The book is being read by me

But with the gerundive of obligation, Latin normally uses the dative of agent instead:

• Mihi liber legendus est = I have to read the book / The book must be read by me

So:

• ordinary passive → often a me
• gerundive of obligation → usually mihi

That is one of the key things learners have to get used to.

Its basic meaning here is simply this:

• hic liber = this book

Depending on context, hic can sometimes feel a little more immediate or deictic, like this here book or this book of mine/near me, but in most beginner contexts you should just understand it as this.

So the important point is that hic is a demonstrative adjective modifying liber.

Hodie means today, and it tells you when the obligation applies.

So the sentence means that the reading must be done today.

Latin word order is flexible, so hodie could appear in different places without changing the basic meaning:

• Mihi hic liber hodie legendus est
• Hodie mihi hic liber legendus est
• Mihi hodie hic liber legendus est

The position can change emphasis a little, but the core meaning stays the same.

Because the grammatical subject is liber, which is singular.

In this construction, the verb agrees with the noun that is to be read, not with mihi.

So:

• liber ... legendus est = singular subject, singular verb
• libri ... legendi sunt = plural subject, plural verb

Even though English may focus on I have to, Latin grammar here is centered on the book.

Yes. Latin word order is much more flexible than English word order because the endings show the grammatical relationships.

So all of these could express essentially the same idea:

• Mihi hic liber hodie legendus est
• Hodie mihi hic liber legendus est
• Hic liber mihi hodie legendus est
• Hic liber legendus est mihi hodie

The exact order can affect emphasis, but not the basic grammar.

For example:

• putting hodie earlier may emphasize today
• putting hic liber first may emphasize this book
• putting mihi first may highlight my obligation

The gerundive of obligation usually expresses a fairly strong sense of necessity:

• must be read
• has to be read
• is to be read

In many contexts, must or have to is the best translation.

However, exact force depends on context. In some passages it can feel slightly softer, closer to should, especially if the surrounding context is not very forceful.

Still, as a default understanding, you should treat:

• legendus est

as expressing real obligation or necessity, not just a simple future event.