Learn Hardcore Icelandic: Ég les bók um stærðfræði.

Habitual: Ég les oft. = I read often.
Right now (still fine): Ég les bók um stærðfræði.
If you want to be explicit about “right now,” use the progressive periphrasis: Ég er að lesa bók um stærðfræði.

Why is there no word for “a” before bók?

Icelandic has no indefinite article. Bók on its own usually corresponds to English “a book.” If you want “one book” (numerical emphasis), you can say eina bók (accusative of ein = one).

What case is bók in here, and how can I tell?

Bók is accusative singular because it’s the direct object of les (to read).

For this noun, nominative/accusative/dative singular all look the same: bók
Genitive singular is bókar
Plural is irregular: nominative/accusative bækur, dative bókum, genitive bóka

Why is it um stærðfræði? What case does um take?

Um means “about” (topic) and it governs the accusative. So stærðfræði is in the accusative after um, though this noun looks the same in all singular cases. Other meanings of um include “around/over” in time/place: um helgina (over the weekend), um miðnætti (around midnight).

Could I say Ég er að lesa bók um stærðfræði to emphasize ongoing action?

Yes. That’s the common way to make the progressive aspect explicit in Icelandic. Both are correct:

Ég les bók um stærðfræði.
Ég er að lesa bók um stærðfræði. (clearly “I am reading…”)

Can I say Ég les í bók instead of Ég les bók?

They’re different:

Ég les bók = I read a book (suggests reading the work itself).
Ég les í bók = I read in a book (leafing through, reading parts, not necessarily the whole thing). With your sentence, Ég les í bók um stærðfræði would mean you’re reading in a math book (not necessarily from cover to cover).

How do I pronounce the sentence?

Approximate guide (bold = Icelandic, after the dash is a rough English-like cue):

Ég — “yehg” (initial y sound; the final g can be light)
les — “layss” (long e)
bók — “bohk” (long “oh”; final k unaspirated)
um — “uum” (like the vowel in “put,” short)
stærðfræði — “stairth-fray-thi” (æ like “eye”; ð like the th in “this”; stress on the first syllable of each part: STÆRÐ-FRÆÐI) General tip: Icelandic stress is on the first syllable of words/compounds.

What is the gender and plural of bók?

Bók is feminine. Its plural is irregular:

Singular: bók
Plural: bækur Dative plural: bókum; genitive plural: bóka.

How do you conjugate lesa (to read) in the present and past?

Present: ég les, þú lest, hann/hún/það les, við lesum, þið lesið, þeir/þær/þau lesa
Simple past (preterite): ég las, þú last, hann/hún/það las, við lásum, þið lástuð/lásuð, þeir/þær/þau lásu
Supine: lesið (used with “have”: ég hef lesið = I have read)
Past participle: lesinn (m), lesin (f), lesið (n)

Should stærðfræði be capitalized?

No. Common nouns aren’t capitalized in Icelandic (unless starting a sentence). Stærðfræði “mathematics” is lowercase.

Can stærðfræði take the definite article or be plural?

It’s normally an uncountable, singular, feminine noun. You can use the definite form to refer to “the mathematics” as a specific field/context:

Indefinite: stærðfræði
Definite: stærðfræðin (nom.), stærðfræðina (acc.), stærðfræðinni (dat.), stærðfræðinnar (gen.) It’s not used in the plural.

How would I say “I am reading the book about mathematics”?

Use the definite form of bók:

Ég er að lesa bókina um stærðfræði. (Without the progressive: Ég les bókina um stærðfræði.)

What’s the typical word order here?

Default is Subject–Verb–Object–(other elements): Ég (S) les (V) bók (O) um stærðfræði (PP). Icelandic is verb-second (V2), so if you front something, the finite verb stays in second position:

Í kvöld les ég bók um stærðfræði. (Tonight I am reading a book about mathematics.)

Where does negation go? How would I say “I’m not reading a book about mathematics”?

The negation ekki usually comes right after the finite verb:

Ég les ekki bók um stærðfræði.
Progressive: Ég er ekki að lesa bók um stærðfræði.

Is um always the right word for “about”?

For topic “about,” yes, um is the default: bók um stærðfræði (a book about mathematics). Alternatives like varðandi (“regarding”) are more formal and often used in writing, not typically with book topics. Don’t use af for this meaning.

What’s a natural way to ask “What book are you reading?” in Icelandic?

Hvaða bók ertu að lesa? (using the progressive)
Without progressive: Hvaða bók lestu? (can be interpreted as present or past depending on context)