The book covers all basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes both for sequential and parallel computer architectures. The book is self-consistent and is intended for people working on implementation and improvement of contact algorithms in a finite element software. The book contains numerous examples and figures to make the material accessible for a broad audience. The book combines extended introductory parts with new developments, so it is accessible for freshmen in computational contact and is of interest for established researchers. Using a new tensor algebra, we introduce some original notions in contact kinematics and extend the classical formulation of contact elements. We discuss robust and efficient contact detection algorithms both for sequential and parallel computer architectures. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are given. Many validation problems and tests are presented.