Scalable Algorithms for Contact Problems 1. Contact Problems and their Solution Part I. Basic Concepts 2. Linear Algebra 3. Optimization 4. Analysis Part II. Optimal QP and QCQP Algorithms 5. Conjugate Gradients 6. Gradient Projection for Separable Convex Sets 7. MPGP for Separable QCQP 8. MPRGP for Bound Constrained QP 9. Solvers for Separable and Equality QP QCQP Problems Part III. Scalable Algorithms for Contact Problems 10. TFETI for Scalar Problems 11. Frictionless Contact Problems 12. Contact Problems with Friction 13. Transient Contact Problems 14. TBETI 15. Mortars 16. Preconditioning and Scaling Part IV. Other Applications and Parallel Implementation 17. Contact with Plasticity 18. Contact Shape Optimization 19. Massively Parallel Implementation Index. This book presents a comprehensive and self contained treatment of the authors’ newly developed scalable algorithms for the solutions of multibody contact problems of linear elasticity. The brand new feature of these algorithms is theoretically supported numerical scalability and parallel scalability demonstrated on problems discretized by billions of degrees of freedom. The theory supports solving multibody frictionless contact problems contact problems with possibly orthotropic Tresca’s friction and transient contact problems. It covers BEM discretization jumping coefficients floating bodies mortar non penetration conditions etc. The exposition is divided into four parts the first of which reviews appropriate facets of linear algebra optimization and analysis. The most important algorithms and optimality results are presented in the third part of the volume. The presentation is complete including continuous formulation discretization decomposition optimality results and numerical experiments. The final part includes extensions to contact shape optimization plasticity and HPC implementation. Graduate students and researchers in mechanical engineering computational engineering and applied mathematics will find this book of great value and interest.