In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms. The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical momenta correspond to derivatives of fields with respect to all world coordinates, not only to time. This book is devoted to the application of this formalism to fundamental field models including gauge theory, gravitation theory, and spontaneous symmetry breaking. All these models are constraint ones. Their Euler–Lagrange equations are underdetermined and need additional conditions. In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density. The general procedure for describing constraint systems with quadratic and affine Lagrangian densities is presented.Contents:Geometric PreliminaryLagrangian Field TheoryMultimomentum Hamiltonian FormalismHamiltonian Field TheoryField Systems on Composite ManifoldsReadership: Researchers and postgraduates in mathematical physics, gauge theory, gravitation and Hamiltonian dynamics.Key Features:Explores coastal prediction based on simple mathematical concepts, validated by coastal engineering practiceConsiders the practical knowledge and experience of many influential people in the field over the past century