Stochastic Canonical Equation of Multidimensional Nonlinear Dissipative Hamiltonian Dynamical Systems; Fundamental Examples of Nonlinear Dynamical Systems and Associated Second Order Equation; Brief Review of Probability and Random Variables; Probabilistic Tools I. Classical Stochastic Processes; Probabilistic Tools II. Mean-Square theory of linear integral transformations and of linear Differential Equations; Probabilistic Tools III. Diffusion Processes and Fokker-Planck Equation; Probabilistic Tools IV. Stochastic Integrals and Stochastic Differential Equations; Stochastic Modelling with Stochastic Differential Equations; FKP Equation for the Dissipative Hamiltonian Dynamical Systems; Stationary Response of Dissipative Dynamical Systems, Existence and Uniqueness, Explicit Solution of an Invariant Measure; Complements for the Normalization Condition, Characteristic Function and Moments of the Invariant Measure; Application II. Multidimensional Linear Oscillators Subjected to External and Parametric Random Excitations; Application III. Multidimensional Nonlinear Oscillators with Inertial Nonlinearity Subjected to External Random Excitations; Application Ill. Multidimensional Nonlinear Oscillators Subjected to External and Parametric Random Excitations; Symplectic Change of Variables in the Multidimensional Unsteady FKP Equation.