I am studying "Knapp, Basic Algebra", at first read, a well to do self-study book. Chapter I looks like this.

1. Division and Euclidean Algorithms 1

2. Unique Factorization of Integers 4

3. Unique Factorization of Polynomials 9

4. Permutations and Their Signs 15

5. Row Reduction 19

6. Matrix Operations 24

7. Problems 30

A manageable 14 pages on the Euclidean Algorithm for integers and polynomials, but dense. Too dense perhaps. Then I had a look at this other book. "Irving, Integers, Polynomials and Rings", have a look at the table of contents.

1 Introduction: The McNugget Problem

Part I Integers

2 Induction and the Division Theorem

3 The Euclidean Algorithm

4 Congruences

5 Prime Numbers

5.1 Prime Numbers and Generalized Induction

5.2 Uniqueness of Prime Factorizations

5.3 Greatest Common Divisors Revisited

6 Rings

7 Euler’s Theorem

8 Binomial Coefficients

Part II Polynomials

9 Polynomials and Roots

10 Polynomials with Real Coefficients

11 Polynomials with Rational Coefficients

12 Polynomial Rings

13 Quadratic Polynomials

14 Polynomial Congruence Rings

Part III All Together Now

15 Euclidean Rings

16 The Ring of Gaussian Integers

17 Finite Fields

I'll guess I stop for a while on my route and do a bit of fun-studying in Irving. If I don't study it now I probably never will. It is a beautiful book. I was almost forgotten that I had it.