Basic machines and mechanisms and kinematic and dynamic problems that arise when designing them. Fundamentals of the matrix equations of motion and equations of connections. Methods for analyzing the kinematics and dynamics of the rigid body system. Methods of synthesis, design, of mechanisms and machines. Fundamentals of the Wolfram Mathematica software package. Fundamentals of MD ADAMS. A system of nonlinear algebraic equations and methods of solving. Kinematics of the planar systems. Constraint equations. Methods for solving the constraint equations and simulations. Kinematics of spatial systems. Constraint equations. Methods for solving the constraint equations and simulations. Differential-algebraic equations and numerical methods for integration. The dynamics of the planar systems. Equations of motion. Methods for solving equations of motion and simulations. Dynamics of spatial systems. Equations of motion. Methods for solving equations of motion and simulations.