Vaikka olin väsynyt, luin e-kirjaa koneessa sen jälkeen kun valot sammuivat.

Vaikka means although / even though. It introduces a contrast:

Vaikka olin väsynyt = Although I was tired

So the sentence sets up a situation where being tired did not stop the action in the main clause.

Finnish often leaves out subject pronouns when the verb ending already shows the person.

• olin = I was
• olimme = we were
• olit = you were

So olin väsynyt is naturally understood as I was tired.
You could say minä olin väsynyt, but that would usually add emphasis, contrast, or a more deliberate tone.

After olla (to be), Finnish uses a predicate adjective.

With a singular subject, that adjective is usually in the nominative singular:

• olin väsynyt = I was tired
• hän oli väsynyt = he/she was tired

The adjective does not change for person. It only changes according to normal agreement patterns. For example, with a plural subject you often get:

• he olivat väsyneitä = they were tired

So väsynyt is the normal singular form here.

It can mean either, depending on context.

Finnish imperfect often covers both:

• English simple past: I read
• English past progressive: I was reading

So luin by itself does not force one choice. In this sentence, because the object is e-kirjaa in the partitive, the sense is often more like an ongoing activity: I was reading an e-book. But English translation depends on context and style.

This is about the object case.

• e-kirjaa is partitive
• e-kirjan is more like a total object

With verbs like lukea (to read), the partitive often shows that the action is:

• ongoing,
• incomplete,
• or viewed as an activity rather than a finished result.

So:

• luin e-kirjaa = I was reading / I read some of an e-book
• luin e-kirjan = I read the whole e-book

In your sentence, e-kirjaa suggests the focus is on the activity of reading, not on finishing the book.

Koneessa is the inessive form of kone.

• kone = machine, device, computer, plane, etc.
• -ssa / -ssä = in

So koneessa literally means in the machine / in the plane / on the computer, depending on context.

If the meaning shown to the learner is on the plane, this makes sense because Finnish often says literally in the plane, while English normally says on the plane.

In Finnish, compounds beginning with a single letter or certain abbreviated elements often use a hyphen.

So:

• e-kirja = e-book
• tv-ohjelma = TV program

In the sentence, e-kirjaa is just the partitive singular form of e-kirja.

It means after, when what follows is a full clause.

Here:

• sen jälkeen = after that / afterwards
• kun = when

Together, sen jälkeen kun valot sammuivat means after the lights went out.

This is a very common Finnish way to express time relations with a whole clause.

Because valot is plural, the verb must also be plural.

• valo = light
• valot = lights

sammuivat is the past tense, 3rd person plural form of sammua, which means to go out / go off / be extinguished.

So:

• valo sammui = the light went out
• valot sammuivat = the lights went out

Finnish often uses the simple past (imperfect) in both clauses when the sequence is already clear.

Here, sen jälkeen kun already tells you the order of events, so valot sammuivat is enough to mean after the lights went out.

Finnish does have a pluperfect, and you could make the time relationship more explicit in some contexts, but in a sentence like this the simple past is the normal and natural choice.

Because Finnish can place the subordinate clause first to set the scene or highlight the contrast.

Starting with Vaikka olin väsynyt gives emphasis to the idea: Even though I was tired...

The rest of the sentence then tells what happened anyway.

You could rearrange Finnish clauses in other ways, but this order is very natural and emphasizes the contrast clearly.