であるFormal or literary だ, Authoritative, Copula

です is often used as the polite form of だ, which is similar in meaning to 'is' or 'to be' in English. It's polite but not overly formal, and it's often used in both speech and writing. In contrast, である is a formal (but not polite) expression mainly used in writing or formal speeches. One key difference is that である can appear in front of nouns in modifying clauses, like in 日本人である留学生 ('an exchange student who is Japanese').

The main difference between だ and である is formality. だ is casual and common in conversation, while である is more formal and mainly used in writing. Both だ and である follow nouns or noun phrases, but である has a more literary tone. である slight differs from the verb ある (to exist) in that である is a fixed connector.

Both are formal forms of 'to be' used in writing. である is the standard formal equivalent of だ, e.g. 彼は学生である ('He is a student.') たる emphasizes qualification or the qualities appropriate to a role, e.g. 指導者たる者 ('A person worthy of being a leader')

がある expresses the existence or possession of inanimate objects, similar to saying 'there is' or 'I have' in English. In contrast, である is comparable to (and is, in fact, an alternate form of) the casual だ or polite です, and is therefore equivalent to the English "it is". In other words, ピアノがある means 'There's a piano' or 'I have a piano', but ピアノである means 'It's a piano' in formal/written language (the spoken polite equivalent would be ピアノです).