Semantics involves giving meaning to logical constants in a formal way. When we talk about truth table semantics, we’re talking about a way to formally interpret (or give meaning to) sentences in the logical language using truth tables. Similarly, algebraic semantics does the same, but using algebras. Proof-theoretic semantics attempts to give meaning in terms of proof rather than truth conditions.
forallx: Cambridge book - Covers both truth-functional logic and first-order logic, introducing students to semantics and to a Fitch-style natural deduction system.