Learn Hardcore Icelandic: Ég fann bókina undir stólnum í gær. - I found the book under the chair yesterday.

fann is the past‐tense (preterite) form of the strong verb finna (‘to find’). It means “found.” Icelandic strong verbs often change their stem vowel in the past.

How would you say “I find the book under the chair” in the present tense?

Use the present form finn. You get:
Ég finn bókina undir stólnum.

Why is bókina used instead of bók, and what does the -ina ending indicate?

bókina is the definite accusative singular of bók (‘book’). In Icelandic the definite article is added as a suffix. The ending -ina marks feminine gender + definite + accusative case (so it’s “the book,” not “a book”).

Could I say Ég fann bók undir stólnum í gær to mean “I found a book under the chair yesterday”?

Yes. Omitting the definite article suffix gives you the indefinite form bók.
Ég fann bók undir stólnum í gær = “I found a (some) book under the chair yesterday.”

Why is stólnum used after undir instead of stóll or stólinn?

When undir expresses location (“under where?”), it takes the dative case.
• stólnum = dative definite singular of stóll + article (stól- +inum → -num).
stólinn would be nominative definite (“the chair” as subject), not dative.

What case would undir take if you wanted to express motion (“to under the chair”)?

Then undir takes the accusative. You’d say undir stólinn, though in practice “going under” is less common than simply “under.”

Why is there í before gær, and can you drop it?

gær is indeclinable, but to say “yesterday” you normally use í gær (literally “in yesterday”). Saying just gær sounds incomplete or poetic in modern usage.

Can I move í gær to the front of the sentence? What happens to word order?

Yes. Icelandic follows the V2 rule (finite verb in second position). So you can say:
Í gær fann ég bókina undir stólnum.
Notice the verb fann stays in position 2, and the subject ég follows it.

Why do we need the pronoun ég? Could it be omitted?

Subject pronouns can be dropped only if the verb form unambiguously marks person. In the present tense finn is clearly first‐person, but in the past fann is identical for first‐ and third‐person singular (hann fann = “he found”), so you need ég for clarity: Ég fann…