This short book is based on a lecture-course on the randomly forced two-dimensional Navier-Stokes Equation (2D NSE) and two-dimensional statistical hydrodynamics which the author taught at ETH-Ziirich during the winter term of the year 2004/2005. The goal of the course was to review recent progress in the qualitative theory of randomly forced nonlinear PDE (especially, the 2D NSE), and discuss applications of the corresponding results to 2D statistical hydrodynamics, including 2D turbulence. The book, as well as the lecture-course, is aimed at people with some background in PDE, or in probability, or in physics. For the benefit of the last two groups of readers we included in the book a section on deterministic 2D NSE.