1 Introduction
2 Multilevel Iterative Solvers
2.1 Direct and Iterative Solvers
2.2 Subspace Correction Schemes
2.3 Multigrid and Multilevel Methods
2.4 Domain Decomposition Methods
2.5 Sparse Grid Solvers
3 Adaptively Refined Meshes
3.1 The Galerkin Method, Finite Elements and Finite Differences
3.2 Error Estimation and Adaptive Mesh Refinement
3.3 Data Structures for Adaptively Refined Meshes
4 Space-Filling Curves
4.1 Definition and Construction
4.2 Partitioning
4.3 Partitions of Adaptively Refined Meshes
4.4 Partitions of Sparse Grids
5 Adaptive Parallel Multilevel Methods
5.1 Multigrid on Adaptively Refined Meshes
5.2 Parallel Multilevel Methods
5.3 Parallel Adaptive Methods
6 Numerical Applications
6.1 Parallel Multigrid for a Poisson Problem
6.2 Parallel Multigrid for Linear Elasticity
6.3 Parallel Solvers for Sparse Grid Discretisations
Concluding Remarks and Outlook.