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This book is intended to illustrate the fluctuating behaviour of a small machanical system in tight interaction with a heat bath, thereby experiencing frictional forces and stochastic random forces. The model is a one-dimensional classical mechanical system described by Langevin equation including inertia. The equation of motion is reduced to first order in time by solving the appropriate Hamilton-Jacobi equation with friction. The two-point configurational transition probability density is recast into the form of a functional integral over the exponential of the action, and this expression is confronted with the similar one obtained from statistical thermodynamical principles. This work is intended to represent a contribution to understanding the thermodynamical and statistical mechanical properties of low dimensional systems strongly interacting with the environment, which may be polymers, biological macromolecules or nanoscale devices.