This book elucidates how Finite Element methods look like from the perspective of Greens functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Greens functions and how approximating of Greens functions. It discusses in detail the discretization error and shows that are coherent with the strategy of goal oriented refinement. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.