An introduction to chordal graphs and clique trees -- Cutting down on fill using nested dissection: Provably good elimination orderings -- Automatic Mesh Partitioning -- Structural representations of Schur complements in sparse matrices -- Irreducibility and primitivity of Perron complements: Application of the compressed directed graph -- Predicting structure in nonsymmetric sparse matrix factorizations -- Highly parallel sparse triangular solution -- The fan-both family of column-based distributed Cholesky factorization algorithms -- Scalability of sparse direct solvers -- Sparse matrix factorization on SIMD parallel computers -- The efficient parallel iterative solution of large sparse linear systems