だ

だ is the plain-register counterpart of です — used between close friends, family, in internal monologue, in declarative writing, and in subordinate clauses. With nouns and na-adjectives only: 学生だ, 静かだ. I-adjectives never take だ — "it's cold" in plain is just 寒い, not 寒いだ.

だ conjugates: じゃない (plain negative), だった (plain past), じゃなかった (plain past negative). Compared to です, だ is the form you'll see in books, internal thought, song lyrics, and casual speech among intimates. Using だ with someone you've just met is rude; using です with your best friend can feel cold.

In subordinate clauses (before と, から, けど, etc.) Japanese typically uses だ regardless of the matrix-clause register: 学生だと思います — "[I] think [they] are a student" (polite matrix, plain subordinate). Knowing when to drop だ — before な, の, です — is part of the conjugation grammar.