Discussion material and exercises related to pre-algebra groups are provided in this five chapter manual. Chapter 1 (mappings) focuses on restricted domains, order of operations (parentheses and exponents), rules of assignment, and computer extensions. Chapter 2 considers finite number systems, including binary operations, clock arithmetic, properties of operational systems, multiplicative systems, and subtraction/division. Other operational groups are considered in chapter 3. Additional topics include the cancellation law, non-commutative groups, and designs from finite systems. Chapter 4 focuses on integers, discussing set of integers, (Z,+) as a commutative group, subtraction, multiplication/division, order of operations, exponents, and absolute value. Transformational geometry is the major focus of chapter 5. Topics discussed in this chapter include: symmetry, plotting points, translations, translations and groups, line reflections, rotations, isometries, and dilation. Each chapter concludes with a set of review questions. In addition, a set of cumulative review questions for chapters 1-3 is included. (JN)