In this chapter, Vectors are introduced. Vector algebra is covered to include vector addition/subtraction and vector multiplication. The utility of vectors is demonstrated by using them to derive geometrical theorems. The Einstein summation convention and index notation are introduced, and these techniques are used to develop numerous identities involving vector (cross) products and scalar (“dot”) products. The Levi-Civita tensor and the Kronecker delta are shown to be indispensable tools when using the Einstein summation convention and index notation. In-chapter examples and end-of-chapter problems are included to reinforce introduced concepts and to give readers a chance to practice the relevant mathematics.