Learn Hardcore Russian: Я удивляюсь, как быстро растут деревья весной. - I am surprised at how quickly trees grow in spring.

In Russian, you put a comma between the main clause and any subordinate clause. Here, Я удивляюсь is the main clause and как быстро растут деревья весной is a subordinate clause introduced by как, so you separate them with a comma.

Why is как used here instead of что?

как introduces an indirect question of manner (“how quickly”), whereas что would introduce a statement (“that the trees grow”). You say как быстро растут... to ask or wonder “how fast they grow,” not just to state “that they grow.”

I thought удивляться takes a dative object like тому. Why is тому missing before как?

You’re right that удивляться normally governs the dative (e.g. удивляться чему-то). When you attach a subordinate clause, you can optionally insert тому (Я удивляюсь тому, как быстро…), but in colloquial and neutral style it’s perfectly fine to drop тому and go straight to как. Both versions are correct.

Why is весной in the instrumental case and not the prepositional?

When indicating time when with seasons (or parts of the day), Russian often uses the instrumental case without a preposition. So “in spring” becomes весной (instrumental), not весне (prepositional).

Can I change the word order in the subordinate clause, for example to Я удивляюсь, как деревья быстро растут весной?

Yes. Russian is flexible. Placing быстро after деревья slightly shifts the emphasis onto деревья, whereas как быстро растут деревья emphasizes the speed of growth. Both word orders are grammatically correct.

What’s the difference between Я удивляюсь and Меня удивляет in expressing surprise?

They mean almost the same (“It surprises me”), but grammatically differ:

Я удивляюсь uses an intransitive verb with я as subject (“I marvel”).
Меня удивляет is an impersonal construction—меня is in the accusative and удивляет acts like a transitive verb (“It surprises me”).
Stylistically, the nuance is very small.

Why is the verb растут (imperfective) used here instead of a perfective like вырастут?

расти (imperfective) describes an ongoing process: “are growing.” A perfective like вырасти would express a completed action (“will grow up” or “have grown up”). Since you’re marveling at the process of growth in spring, the imperfective растут is the natural choice.

Why is деревья in the nominative plural? Could it be another case?

деревья is the subject of растут, so it must be in the nominative plural. If you wanted “I watch the trees,” for example, trees would be in the accusative (я смотрю на деревья), but here they perform the action “grow.”

Could the subordinate clause come before the main clause, as in Как быстро растут деревья весной, я удивляюсь?

It’s grammatically possible to front the subordinate clause, but it sounds marked or literary. The more neutral word order is to state the main clause first (Я удивляюсь), then the subordinate clause explaining what surprises you.