Utan din underskrift kan vi inte skicka avtalet i dag.

Because Swedish often puts a time phrase, place phrase, or condition at the beginning of the sentence for emphasis. Here Utan din underskrift means without your signature, and it sets up the condition first.

Starting with this phrase makes the sentence feel a bit like: Without your signature, we cannot send the contract today.

This is because of the Swedish V2 rule. In a main clause, the finite verb must come in the second position.

Here, the first position is the whole phrase Utan din underskrift, so the verb kan must come next:

Utan din underskrift | kan | vi | inte skicka avtalet i dag.

If the sentence began with vi, then you would say:

Vi kan inte skicka avtalet i dag utan din underskrift.

Both are grammatical, but the original sentence emphasizes the condition first.

In Swedish main clauses, inte usually comes after the finite verb and usually after the subject too when the verb has moved to second position.

So here the order is:

kan + vi + inte

That gives:

kan vi inte

Compare:

• Vi kan inte skicka avtalet i dag.
• Utan din underskrift kan vi inte skicka avtalet i dag.

A useful contrast is subordinate clauses, where inte comes earlier:

• ...att vi inte kan skicka avtalet i dag

So the placement of inte depends on clause type.

Because underskrift is an en-word in Swedish:

• en underskrift = a signature

For en-words, the possessive is:

• min / din / sin

For ett-words, it would be:

• mitt / ditt / sitt

So:

• din underskrift = your signature
• but ditt avtal would be possible, because avtal is an ett-word

After a possessive like min, din, hans, hennes, vår, Swedish normally uses the indefinite form of the noun, not a separate article and not the definite ending.

So you say:

• din underskrift
• min bok
• hans bil

Not:

• din underskriften
• din en underskrift

This is normal Swedish grammar.

It is singular indefinite.

The basic forms are:

• en underskrift = a signature
• underskriften = the signature
• underskrifter = signatures
• underskrifterna = the signatures

In the sentence, din underskrift uses the basic singular form because it follows a possessive.

Because avtalet is the definite form and means the contract.

The noun is:

• ett avtal = a contract
• avtalet = the contract

So the sentence is referring to a specific contract that both sides already know about.

This is very common in Swedish: the definite article is usually added as an ending on the noun.

Because avtal is an ett-word:

• ett avtal

For many ett-words, the definite singular ending is -et:

• ett avtal → avtalet
• ett hus → huset

So -et here is the Swedish way of saying the.

Both i dag and idag are used in modern Swedish. They mean the same thing: today.

Many textbooks and more traditional writing prefer i dag, while idag is also very common in everyday use. So as a learner, you should recognize both.

Here utan is a preposition meaning without:

• utan din underskrift = without your signature

It is followed by a noun phrase.

Be aware that utan can also have another use in Swedish, meaning something like but rather in some sentences, but that is not what it is doing here. In this sentence, it simply means without.

Yes, absolutely. That version is also correct.

The difference is mainly emphasis:

• Utan din underskrift kan vi inte skicka avtalet i dag.
  This emphasizes the missing signature first.

• Vi kan inte skicka avtalet i dag utan din underskrift.
  This is a more neutral, straightforward word order.

So the original sentence is not strange; it is just using fronting for emphasis.

In Swedish, a short phrase at the beginning of the sentence usually does not need a comma.

So this is normal:

Utan din underskrift kan vi inte skicka avtalet i dag.

English often uses commas a bit more freely in similar sentences, but Swedish usually keeps this kind of sentence without one.