The main theme of this paper is the development of a “hybrid” multigrid approach, applicable to discretized partial differential equations where uniform refinement is applied to some unstructured, “base” mesh of moderate size. The proposal is to use algebraic multigrid to coarsen the base mesh and maintain efficient treatment of the unstructured aspects of the problem, but to use classical geometric multigrid components for levels of the multigrid hierarchy that come from uniform refinement. To motivate their algorithmic choices, the author devote some attention to the choice of consistent interpolation and restriction operators, with respect to finite-element, finite-difference, or finite-volume discretizations, accurately summarizing the well-known choices made in these cases. A multistep Jacobi-like relaxation scheme is proposed, with weights chosen using Chebyshev polynomials. The presented numerical results are generally acceptable, although the authors fail to present a numerical example where their strategy outperforms standard geometric multigrid.