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Higher Order Mortar Finite Elements with Dual Lagrange Multipliers presents the theories and applications of higher order nonconforming finite element techniques based on the mortar method. As the mortar finite element method is based on replacing the usual point-wise continuity condition by a weak matching condition, the dual Lagrange multipliers allow an efficient and easy realization of this weak matching condition. In addition to the main contribution of this work on the construction of dual Lagrange basis functions for higher order finite elements in two and three dimensions, there are also some interesting theoretical advancement and applications of the mortar finite elements. Moreover, a popular three-field formulation in elasticity, the Hu-Washizu principle, is analysed for linear elasticity and extended to non-linear elasticity. Mortar techniques are applied to analyse interface problems for elliptic partial differential equations and to solve different coupled problems coming from physical and engineering applications.