Þó að ég sé þreyttur eftir langan dag, finnst mér alltaf gaman að horfa á hana spyrna boltanum.

Because þó að often introduces a clause that takes the subjunctive in Icelandic.

• er = present indicative of vera = am / is / are
• sé = present subjunctive of vera

So þó að ég sé þreyttur is the normal way to say although I am tired.

For a learner, the key point is:

• þó að
  • very often subjunctive
• therefore ég sé, not ég er

You may sometimes encounter þó að ég er in less careful or more colloquial usage, but sé is the standard form here.

Þó að is a conjunction meaning although, even though, or though.

It introduces a subordinate clause that gives a contrast:

• Þó að ég sé þreyttur ... = Although I am tired ...

In this sentence, it sets up the contrast between:

• being tired after a long day
• still enjoying watching her kick the ball

Because þreyttur agrees with the speaker, ég, in gender, number, and case.

Here it is a predicate adjective after vera, so it is in the nominative singular.

If the speaker is:

• masculine: ég er / sé þreyttur
• feminine: ég er / sé þreytt
• plural: different plural forms would be used

So þreyttur tells you the speaker is grammatically masculine.

Because the preposition eftir takes this case here, so langur dagur changes to langan dag.

What is happening:

• dictionary form: langur dagur = a long day
• after eftir in this sentence: langan dag

So:

• eftir langan dag = after a long day

This is a good example of how Icelandic prepositions affect case. The adjective and noun both change form to match the case required.

Because mér finnst is a very common Icelandic way to say I think, I feel, or I find something in a personal-experience sense.

Literally, it is closer to:

• to me, it seems / feels

So:

• mér finnst gaman = I find it fun / I enjoy it

Important grammar point:

• mér is dative
• this construction is not built like a normal English I + verb + object sentence

That is why mér appears instead of ég.

It is a very common Icelandic pattern meaning I enjoy ... or I think it is fun to ...

Structure:

• mér finnst gaman að + infinitive

So here:

• mér finnst alltaf gaman að horfa ...
  = I always enjoy watching ... = It always feels fun to me to watch ...

A more literal breakdown is:

• mér = to me
• finnst = seems / feels
• gaman = fun
• að horfa ... = to watch ...

Because Icelandic follows a verb-second pattern in main clauses.

The first part of the sentence, Þó að ég sé þreyttur eftir langan dag, is a subordinate clause placed first. Once that whole clause takes the first position, the finite verb of the main clause comes next:

• Þó að ég sé þreyttur eftir langan dag, finnst mér ...

So the order is:

1. fronted clause
2. finite verb of the main clause
3. the rest

This is very normal Icelandic syntax. English does not work this way as consistently, so it often feels unusual at first.

Because the verb is horfa á, which means watch or look at.

In Icelandic, you do not normally just say horfa hana. You say:

• horfa á einhvern / eitthvað = watch someone / something, look at someone / something

So:

• að horfa á hana = to watch her

Also, hana is in the form used after á here, which is why you get hana and not henni.

Because Icelandic can use a structure like watch someone do something, just like English.

So:

• að horfa á hana spyrna boltanum

means:

• to watch her kick the ball

The idea is:

• hana is the person being watched
• spyrna boltanum tells you what she is doing

This is similar to English:

• watch her kick the ball
• not watch her to kick the ball

So the lack of að before spyrna is normal.

Because spyrna takes a dative object in this usage.

That means the noun after it is not in the accusative form you might expect from English. Instead:

• boltinn = the ball
• boltanum = the ball in dative singular

So:

• spyrna boltanum = kick the ball

This is an example of lexical case, which is very common in Icelandic: some verbs simply require a particular case, and learners have to memorize that with the verb.

Alltaf means always.

Here it modifies the whole idea of finding it fun:

• finnst mér alltaf gaman = I always find it fun

Its placement is natural Icelandic word order:

• finite verb first in the main clause: finnst
• then mér
• then the adverb alltaf
• then gaman

So the sentence is not saying that the watching is somehow always happening; it is saying that this is something the speaker always enjoys.