Basta che tu abbia la tessera, e il bibliotecario ti presta il libro.

Basta che means as long as, provided that, or more literally it is enough that.

So Basta che tu abbia la tessera means something like:

• As long as you have the card
• Provided you have the card
• You only need to have the card

It emphasizes that this one condition is sufficient.

Here che is a conjunction introducing a subordinate clause.

In basta che + subjunctive, Italian expresses the idea of a condition being enough:

• Basta che arrivi in tempo = As long as you arrive on time
• Basta che tu abbia la tessera = As long as you have the card

So che is not that in the usual English sense here. It is just part of the fixed pattern basta che.

Because basta che normally requires the subjunctive in Italian.

So:

• tu hai = indicative
• tu abbia = present subjunctive

After expressions like basta che, Italian usually uses the subjunctive because the clause expresses a condition, requirement, or possibility rather than a simple statement of fact.

That is why you get:

• Basta che tu abbia la tessera

not:

• Basta che tu hai la tessera

Abbia is the present subjunctive of avere.

Here is the present subjunctive of avere:

• che io abbia
• che tu abbia
• che lui/lei abbia
• che noi abbiamo
• che voi abbiate
• che loro abbiano

In the sentence, tu abbia means you have in the subjunctive.

No, tu is not strictly necessary. Italian often drops subject pronouns because the verb ending already shows the subject.

So these both work:

• Basta che tu abbia la tessera
• Basta che abbia la tessera

Using tu can add a little emphasis or clarity, especially for learners or in speech where the speaker wants to be explicit.

La tessera means the card or the membership card. In context, it is understood which card is meant.

Italian often uses the definite article where English might prefer a possessive or a more specific phrase. So depending on context, la tessera could be understood as:

• the card
• your card
• the library card / membership card

If the speaker wanted to be more explicit, they could say:

• la tessera della biblioteca = the library card
• la tua tessera = your card

But la tessera is perfectly normal if the context already makes it clear.

Ti means to you.

So:

• prestare = to lend
• ti presta = lends to you
• il libro = the book

Literally, il bibliotecario ti presta il libro is:

• the librarian lends the book to you

Italian uses an indirect object pronoun before the verb:

• mi = to me
• ti = to you
• gli/le = to him/her
• ci = to us
• vi = to you all
• gli = to them

So ti presta il libro is the natural Italian word order.

It means lend, not borrow.

That is an important difference for English speakers:

• prestare = to lend
• prendere in prestito = to borrow

So:

• Il bibliotecario ti presta il libro = The librarian lends you the book
• Tu prendi in prestito il libro = You borrow the book

Because the subjunctive is triggered by basta che only in the subordinate clause:

• che tu abbia la tessera

The second part, il bibliotecario ti presta il libro, is the main clause and is presented as a normal result or fact, so the indicative is used.

In other words:

• abbia = subjunctive, because it depends on basta che
• presta = indicative, because it states what happens

Italian often uses the present tense to express a regular consequence or something that will happen in that situation.

So il bibliotecario ti presta il libro can mean:

• the librarian lends you the book
• the librarian will lend you the book

The present here sounds natural because it describes what normally happens once the condition is met.

If you wanted to sound more explicitly future-oriented, you could also say:

• il bibliotecario ti presterà il libro

But the present tense is very common in Italian for this kind of meaning.

Not necessarily. The comma is mostly a punctuation choice here.

• Basta che tu abbia la tessera e il bibliotecario ti presta il libro.
• Basta che tu abbia la tessera, e il bibliotecario ti presta il libro.

Both can be understood. The comma creates a slight pause and separates the two parts more clearly. In many cases, Italian writers would simply leave it out.

Yes, it is understandable and natural enough, especially in conversation. It clearly means that having the card is the only real requirement.

That said, depending on context, Italians might also say:

• Se hai la tessera, il bibliotecario ti presta il libro.
  This is a bit more straightforward: If you have the card, the librarian lends you the book.

• Basta avere la tessera e il bibliotecario ti presta il libro.
  This is a slightly more general version: You just need to have the card...

• Basta che tu abbia la tessera e il bibliotecario ti presterà il libro.
  This makes the future meaning more explicit.

So the original sentence is fine, but there are several natural ways to express the same idea.