1 Introduction -- 2 Basics of mathematics -- 3 Kinematic performance analysis and optimization of parallel manipulators without actuation redundancy -- 4 Motion/Force transmission performance analysis and optimization of parallel manipulators with actuation redundancy -- 5 Motion/Force constraint performance analysis and optimization of overconstrained parallel manipulators with actuation redundancy -- 6 Elastostaic stiffness evaluation and optimization of parallel manipulators -- 7 Multi-objective optimization of parallel manipulators using game algorithm -- 8 Hybrid algorithm for multi-objective optimization design of parallel manipulators -- 9 Multi-objective optimization design and sensitivity analysis of parallel manipulators -- 10 Multi-objective optimization design of parallel manipulators based on the principal component analysis.