Multigrid is one of the few optimal methods for solving systems of equations arising from the discretization of partial differential equations as well as a wide variety of related problems on graphs. In this tutorial we will introduce the key ingredients of the multigrid method (smoothing and coarse grid correction), explain their complementarity (they don't work well alone), and describe the most common cycling strategies. We will present the concepts and motivating analysis using a simple geometric approach to solving the linear system arising from the discretization of the diffusion equation on structured orthogonal grids. Then we will highlight the elements of the algorithm that have been advanced to provide robustness and flexibility for more general problems (e.g., operator dependent interpolation, galerkin coarse grid operators, and algebraic methods), noting that these topics will be covered in more detail in the subsequent tutorials. Finally, we'll touch on the popular and powerful use of multigrid as a preconditioner for Krylov methods such as the conjugate gradient method.