This is Part 1 of the second course in a series which focuses on building fundamental mathematical structures. Topics considered in this book include: an introduction to mathematical logic and mathematical proof, a continuation of the study of groups, an introduction to axiomatic affine geometry, fields, the real number system, and coordinate geometry. The discussion of groups contains an example of a non-commutative group, theorems about groups, and the concept of isomorphism. Axioms for an affine geometry are given together with some logical consequences of these axioms and finite and infinite models for the axioms. The chapters on fields and the real number system include solving equations and inequalities, properties of the real number system and calculation with irrational numbers. (FL)