Lecture 2022-02-10. The language of number theory, and the Peano axioms for it. The last axiom: the principle of mathematical induction. Different forms of it. Using induction for establishing different claims: sum of first n numbers; sum of first odd number; evenness of n^2+n; dispensing envelopes in packs of 12 and 5; tiling the punctured 2^n x 2^n plane grid with punctured triominoes.