This presentation is an updated reincarnation of the tutorials Bill gave at Copper Mountain in 1987 and 1989. The 1987 tutorial led to the publication of the popular book, A Multigrid Tutorial (SIAM books), which has served as the introduction to multigrid for a good many workers in the field. Assuming no familiarity with multigrid, the tutorial introduces multigrid from first principles, examining basic iterative methods, coarse-grid correction, two-level approaches, and extending to multigrid methods.

Part I consists of the following components:

• Model Problems
• Basic Iterative Methods
• Elements of Multigrid
• Performance
• Some Theory

Part II consists of the following components:

• Neumann boundary conditions
• Anisotropic operators
• Variable mesh problems
• Variable coefficients
• Multigrid for Nonlinear problems: introduction to FAS
• Grid refinement: introduction to FAC
• Overview of algebraic multigrid (AMG)