Linear algebra is ubiquitous in mathematics and the natural and social sciences. It is the study of linear transformations. These kind of transformations are, in some sense, the building blocks for almost all interesting functions (since a derivative is a linear transformation) and are closely related to geometry in all dimensions. Every linear transformation can be expressed using a matrix, but more than one matrix might correspond to the same linear transformation. We'll explore the relationship between matrices, linear transformations, and geometry. Along the way, we'll encounter many different applications of linear algebra and even begin to think differently about mathematics itself.