Learn Hardcore Russian: Мне удобно работать за компьютером у окна. - It is convenient for me to work at the computer by the window.

Russian often expresses feelings/states like удобно, холодно, жарко, скучно with a dative experiencer: literally To me it is convenient…
So мне удобно is the normal pattern. Using я would require a different construction (e.g., я чувствую себя удобно/комфортно, which is less common and sounds different).

What part of speech is удобно here, and why does it end in -о?

Here удобно is a predicative adverb/state word (often taught as a “category of state” word), used to describe a general state: it’s convenient.
The -о ending is typical for these predicate words (compare интересно, трудно, можно, нельзя).

Is there an implied это in the sentence?

Yes, conceptually it’s like Мне (это) удобно…, but Russian usually omits это in this kind of structure. Adding это is possible but often sounds heavier and more emphatic.

Why is работать an infinitive? Could it be a finite verb?

After predicative words like удобно, Russian commonly uses an infinitive to name the action that is convenient: удобно работать, приятно читать, сложно понять.
A finite verb would force a different structure, e.g. Мне удобно, когда я работаю… (a clause with когда).

Why is it за компьютером and not на компьютере?

They mean different things in Russian:

за компьютером = physically at the computer / seated at the workstation (location + posture/activity)
на компьютере = doing something on the computer as a platform/tool (e.g., работать на компьютере, играть на компьютере)
In this sentence, за компьютером emphasizes being positioned at the computer.

Why does компьютер become компьютером?

Because the preposition за (in the meaning “at/behind, positioned at”) requires the instrumental case:
за + instrumental → за столом, за рулём, за компьютером.

What does у окна mean grammatically, and why is окна in genitive?

у expresses being by/near something and governs the genitive case:
у + genitive → у окна, у дома, у двери.
So окно becomes окна (genitive singular).

Could I also say около окна or возле окна instead of у окна?

Yes. All mean “near the window,” but with slightly different flavor:

у окна is very common, neutral, and often implies close proximity (right by it)
около окна is neutral “near”
возле окна is also “near,” sometimes a bit more conversational
All three take the genitive.

Is the word order fixed? Can I move у окна earlier?

Russian word order is flexible. You can move phrases for emphasis or flow:

Мне удобно работать за компьютером у окна. (neutral)
Мне удобно работать у окна за компьютером. (focus slightly more on “by the window”)
У окна мне удобно работать за компьютером. (fronting у окна emphasizes the location)
The grammar stays the same; the nuance/what feels “highlighted” changes.

Can мне be omitted?

Sometimes, yes—if it’s obvious whose perspective it is:

Удобно работать за компьютером у окна. can sound like a general statement (“It’s convenient to work…”).
But if you mean specifically “for me,” keeping мне is clearer and more natural.

Why is работать imperfective? Could it be поработать?

работать (imperfective) fits a general, ongoing activity: “working (in general / habitually).”
поработать (perfective) would shift meaning toward “work for a while / do some work (as a bounded event).” With удобно, imperfective is usually the default unless you specifically mean a short, one-time session.