Hur trött hon än är vill hon gärna fotografera familjen på födelsedagar.

It is a set pattern meaning no matter how tired she is or however tired she is.

So:

• hur = how
• trött = tired
• hon är = she is
• än helps create the no matter / however meaning in this structure

This pattern is very common in Swedish:

• Hur dyrt det än är ... = No matter how expensive it is ...
• Vad han än säger ... = Whatever he says ...
• Var hon än bor ... = Wherever she lives ...

So here, hur ... än is not being translated word-for-word in a simple way; it works as one grammatical expression.

Good question. Än often does mean than:

• Hon är längre än jag. = She is taller than me.

But in this sentence, än is doing something different. In patterns like:

• hur ... än
• vad ... än
• vem ... än
• var ... än

it helps express no matter..., however..., whatever..., whoever..., wherever...

So in hur trött hon än är, än is not than. It is part of a fixed concessive pattern.

Because this part behaves like a subordinate clause, and Swedish subordinate clauses normally keep the subject before the finite verb.

So you get:

• hon ... är

not

• är ... hon

Structure:

• hur trött = how tired
• hon = she
• än
• är = is

That gives:

• Hur trött hon än är

This is one of those places where English speakers often want to copy English word order too directly. Swedish does not do that here.

Because Swedish uses the V2 rule in main clauses: the finite verb must come in the second position.

The sentence begins with a fronted clause:

• Hur trött hon än är

After that, the main clause starts. Since the first position is already taken by the whole opening clause, the finite verb must come next:

• vill

and then the subject:

• hon

So:

• Hur trött hon än är, vill hon gärna fotografera familjen ...

If you started directly with the main clause, you would say:

• Hon vill gärna fotografera familjen på födelsedagar.

But once you move another element to the front, inversion happens:

• På födelsedagar vill hon gärna fotografera familjen.
• Hur trött hon än är vill hon gärna fotografera familjen.

Gärna is a very common Swedish word that often means something like:

• gladly
• with pleasure
• willingly
• with vill, often would like to

In this sentence, vill gärna fotografera is best understood as:

• likes to photograph
• would very much like to photograph
• is happy to photograph

It adds a sense that she does it willingly or with pleasure.

Compare:

• Hon vill fotografera familjen. = She wants to photograph the family.
• Hon vill gärna fotografera familjen. = She would like to / is happy to photograph the family.

So gärna softens the statement and makes it sound more natural and willing.

Both are possible, but they are not exactly the same.

• vill gärna fotografera = would like to photograph / is happy to photograph
• gillar att fotografera = likes photographing / likes to photograph

Vill gärna often sounds more like willingness in a situation or habit, while gillar att focuses more directly on enjoyment.

So in this sentence, vill gärna fotografera familjen på födelsedagar suggests that, even if she is tired, she is still willing and keen to do it.

No preposition is needed here. In Swedish, fotografera can take a direct object:

• fotografera familjen = photograph the family

That is completely normal.

You may also hear other expressions, such as:

• ta bilder på familjen = take pictures of the family
• ta kort på familjen = take photos of the family

But fotografera familjen is correct and straightforward.

Familjen means the family, and here it works fine because the context makes it clear whose family is meant.

Swedish often uses the definite form where English might also naturally say the family.

You could say sin familj in some contexts if you specifically wanted to emphasize her own family, but it is not necessary here.

So:

• fotografera familjen = photograph the family

is the natural choice.

Because på is commonly used for events, occasions, and days in Swedish.

Here på födelsedagar means:

• on birthdays
• at birthday celebrations, depending on context

Some common parallels:

• på julen / på julafton
• på festen = at the party
• på mötet = at the meeting

So på is the normal preposition here.

Because it is being used in a generic sense: birthdays in general.

• på födelsedagar = on birthdays / at birthdays

This is similar to English, where you can also use a bare plural for general meaning.

If you said på födelsedagarna, that would sound more like specific birthdays already known from context, for example the birthdays we usually celebrate.

So the indefinite plural here gives the broad, habitual meaning.

Most naturally, it sounds like a general habit.

That feeling comes especially from:

• på födelsedagar = on birthdays, in general
• the overall present-tense statement

So the sentence suggests something like: whenever birthdays happen, she likes to photograph the family, even if she is tired.

Yes. Swedish has other ways to express a similar idea, for example:

• Även om hon är trött vill hon gärna fotografera familjen på födelsedagar.
  = Even if she is tired, she still wants to photograph the family on birthdays.

But hur trött hon än är is stronger and more idiomatic for no matter how tired she is.

So:

• även om hon är trött = even if she is tired
• hur trött hon än är = no matter how tired she is / however tired she is

The original sentence sounds more emphatic.

A comma is often optional here. In modern Swedish, commas are generally used less than in English.

So both of these are possible:

• Hur trött hon än är vill hon gärna fotografera familjen på födelsedagar.
• Hur trött hon än är, vill hon gärna fotografera familjen på födelsedagar.

Many writers would leave the comma out. The sentence is correct either way.