<p style="margin: 0px;"><b></b> This text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each.</p> <p style="margin: 0px;"> </p> <p style="margin: 0px;" sonormal=""><b></b> <b>Number Theory: </b>Induction; Binomial Coefficients; Greatest Common Divisors; The Fundamental Theorem of Arithmetic </p> <b> <p style="margin: 0px;"></p></b> <p style="margin: 0px;" sonormal="">Congruences; Dates and Days. <b>Groups I: </b>Some Set Theory; Permutations; Groups; Subgroups and Lagrange's Theorem; Homomorphisms; Quotient Groups; Group Actions; Counting with Groups. <b>Commutative Rings I: </b>First Properties; Fields; Polynomials; Homomorphisms; Greatest Common Divisors; Unique Factorization; Irreducibility; Quotient Rings and Finite Fields; Officers, Magic, Fertilizer, and Horizons. <b>Linear Algebra: </b>Vector Spaces; Euclidean Constructions; Linear Transformations; Determinants; Codes; Canonical Forms. <b>Fields: </b>Classical Formulas; Insolvability of the General Quintic; Epilog. <b>Groups II: </b>Finite Abelian Groups; The Sylow Theorems; Ornamental Symmetry. <b>Commutative Rings III: </b>Prime Ideals and Maximal Ideals; Unique Factorization; Noetherian Rings; Varieties; Grobner Bases. </p> <p style="margin: 0px;"> </p> <b></b> For all readers interested in abstract algebra.