Mathematics is often described as the language of logic and precision. To truly appreciate its structure and solve problems effectively, students must master some of its most essential foundational concepts. This book has been thoughtfully designed to guide learners through three critical topics that serve as building blocks for deeper mathematical understanding: Order of Operations, Powers, and The GCD and LCM of Integers. In Chapter One, Order of Operations, we explore the rules that govern the sequence in which calculations are performed. Often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this concept is fundamental to interpreting and solving mathematical expressions correctly. Without a solid grasp of this order, even simple problems can lead to confusion and incorrect answers. Chapter Two focuses on Powers. Powers represent repeated multiplication and are vital in expressing large numbers efficiently. This chapter aims to demystify exponents and provide practical tools for computation and problem-solving. In Chapter Three, we introduce The Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of integers-two concepts that are key in simplifying fractions, finding patterns, and solving real-world problems involving cycles and groupings. These topics also provide an early introduction to number theory and offer many opportunities for logical reasoning. Whether you are a student beginning your math journey or a teacher seeking clear explanations and practice exercises for your classroom, this book offers a structured and engaging path forward. Each chapter includes step-by-step examples, helpful illustrations, and practice sections to reinforce learning. We invite you to approach this book with curiosity and confidence. Mathematics is not just about numbers-it's about patterns, reasoning, and discovering the beauty of logic. Let's begin.