Learn Hardcore Russian: Проект уже закончен, и я доволен. - The project is already finished, and I am satisfied.

In Russian, the present-tense verb быть (to be) is normally omitted: Проект (есть) закончен. Using есть here would sound emphatic or книжно (bookish) and is uncommon in everyday speech. The meaning is finished is carried by the predicate form закончен.

What exactly is закончен grammatically?

Закончен is a short-form passive participle (краткое страдательное причастие) from the perfective verb закончить (to finish). Short-form participles are commonly used as predicates to describe a resulting state: The project is finished (as a result).

Why is it закончен (masculine) and not some other ending?

It agrees with проект, which is masculine singular nominative.

проект (masc.) → закончен
feminine: работа закончена
neuter: письмо закончено
plural: дела закончены

What’s the difference between закончен and законченный?