This book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra What if there existed a universal mathematical language that allowed one to make rotations in any dimension with simple formulas to see spinors or the Pauli matrices and their products to solve problems of the special theory of relativity in threedimensional Euclidean space to formulate quantum mechanics without the imaginary unit to easily solve difficult problems of electromagnetism to treat the Kepler problem with the formulas for a harmonic oscillator to eliminate unintuitive matrices and tensors to unite many branches of mathematical physics What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension to play with geometry on a computer as well as to make calculations in robotics raytracing and brain science In addition what if such a language provided a clear geometric interpretation of mathematical objects even for the imaginary unit in quantum mechanics Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it and undergraduate students can master it.