This book provides a starting point for the understanding of Geometric Algebra in a 2D setting as a foundation for the understanding of 3D applications, especially those using the very popular Conformal Geometric Algebra. The focus is on an algebra, called Compass Ruler Algebra. This algebra offers the possibility to compute with circles, lines and point pairs in a very intuitive way. While focusing on 2D, it is easily expandable to 3D computations. The book is divided into three parts: Part I is an easy to understand tutorial with many figures; Part II presents the mathematical background; Part III is dedicated to applications.