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The estimation of hydrodynamic loads and the stochastic nature of ocean wave excitation are fundamental issues that set naval architecture and ocean engineering apart from much of civil engineering. In this new edition of PNA, the presentation attempts to introduce the key topics that all those involved with ocean related engineering should be somewhat familiar with. The presentation also attempts to provide a bridge to more advanced theories and recent developments. This edition significantly expands and supersedes many aspects discussed in the previous version of PNA. The presentation begins by addressing the fundamental approaches to modeling the motions of a ship or offshore platform. These include coordinate systems and transformations, rigid-body equations of motion, the Navier-Stokes equations governing fluid motion, and approaches to their solution. This is followed by a presentation of topics from random process theory that tackles the inescapable problem of the stochastic nature of the ocean and associated parameters of interest. The chapter provides a careful and expansive development of random process theory as applied to marine dynamic responses to waves.