This book is well suited for students interested in learning through self-teaching, or as a supplement to classroom methodologies using conventional texts. The basic principles of algebra are explained in easy to understand detail along with their utilization in mathematical problem solving. Throughout the book, there are detailed descriptions of model problems that show students strategies for analyzing problems and employing algebraic techniques to reach solutions. No previous knowledge of algebra is expected. The book emphasizes that algebra is an extension of the arithmetic structure with which we are all familiar. The use of variables and equations adds great power to that structure for solving real world problems while always adhering to the well understood rules of arithmetic. The goal is for students to truly understand this potent extension of arithmetic and become confidant that the proper application of algebraic principles will always lead to correct solutions. When students truly understand these basic precepts, they will more easily progress to mastering the more complex algebraic configurations in intermediate and advanced algebra.