Jag ska gå till biblioteket även om det regnar.

Ska is often used to talk about the future in Swedish, especially when there is an intention, plan, or expectation.

So Jag ska gå till biblioteket means something like:

• I’m going to go to the library
• I will go to the library

In this sentence, ska suggests a planned action rather than just a neutral future fact.

In Swedish, till means to, and it is needed when you are talking about movement toward a place.

• gå till biblioteket = go to the library

You usually cannot leave out till here. English and Swedish work similarly in this case.

Compare:

• Jag går till skolan = I’m going to school
• Hon sprang till stationen = She ran to the station

The ending -et is the Swedish definite article, attached to the end of the noun.

• ett bibliotek = a library
• biblioteket = the library

Swedish usually puts the at the end of the noun instead of using a separate word like English does.

So:

• till biblioteket = to the library

Även om means even if or even though, depending on context.

In this sentence:

• Jag ska gå till biblioteket även om det regnar
• I’m going to the library even if / even though it’s raining

It introduces a contrast: the speaker will go to the library despite the rain.

You can think of it as showing that the second part does not change the plan in the first part.

Here, det is a dummy subject, just like it in English weather expressions.

• det regnar = it’s raining
• det snöar = it’s snowing

This det does not refer to a specific thing. It is simply required by the grammar.

So this works very much like English:

• It is raining
• Det regnar

Swedish often uses the present tense in time clauses and conditional-type clauses where English might also use the present.

So även om det regnar literally uses present tense:

• even if it rains / even though it is raining

This is normal Swedish. You do not usually need a future form here.

The future idea is already clear from ska in the main clause:

• Jag ska gå... = I’m going to go...

Yes, but the clause itself keeps normal subordinate clause word order.

In även om det regnar:

• det = subject
• regnar = verb

That order is normal.

A useful thing to know is that if the även om clause comes first, the main clause then uses inversion:

• Även om det regnar, ska jag gå till biblioteket.

Notice that ska comes before jag in the main clause after the opening clause. That is standard Swedish word order.

Yes, there is a small difference.

• Jag ska gå till biblioteket... sounds more like a plan, intention, or future action.
• Jag går till biblioteket... can sound more like a present habit, a scheduled action, or sometimes a near-future action depending on context.

In many situations, both could be understood, but ska makes the future plan clearer.

Not in exactly the same way here.

• även om = even if / even though
• fast often means although / though / but

Fast det regnar can work in some contexts, but it is not always the best replacement. Även om is especially good when you mean that something will happen despite a condition.

So in this sentence, även om is the most natural choice for even if/even though it rains.

A natural spoken version would often stress the contrast around även om:

• Jag ska gå till biblioteket även om det regnar.

The important idea is: the rain does not change the plan.

In everyday speech, this sentence sounds completely normal and idiomatic. It is a good model for sentences like:

• Jag ska träna även om jag är trött.
  = I’m going to work out even if I’m tired.

• Vi ska åka även om vädret är dåligt.
  = We’re going to go even if the weather is bad.

Yes, a few very useful patterns:

1. ska + infinitive often expresses future plans

   • Jag ska gå = I’m going to go

2. Movement toward a place usually uses till

   • gå till biblioteket = go to the library

3. The definite article is attached to the noun

   • biblioteket = the library

4. Weather expressions use det

   • det regnar = it’s raining

5. även om introduces a contrast or condition

   • även om det regnar = even if/even though it rains

This one sentence contains several very common Swedish patterns, so it is a great one to learn well.