Preliminaries from Commutative Algebra and Group Theory; Quadratic Forms, Norms and Traces; Polynomials and their Roots; Algebraic Numbers, Rings of Integers; Field Extensions including an introduction to Galois theory; Dedekind Domains; Factorization; Class Numbers, the Unit Theorem; Cyclotomic Extensions; Kronecker-Weber Theorem; Fermat's Last Theorem; Valuations; Archimedean, Non-Archimedean Metrics; Hensel’s lemma; p-adic Number Field, Local Fields; Global Fields; Applications of Algebraic Number Theory.