In this chapter, we review the Lagrangian and Hamiltonian formalisms of classical field theory. We begin by recalling how to formulate Lagrangians for continuous fields and derive the corresponding equations of motion using the variational method. We then introduce classical relativistic fields, starting with the Klein-Gordon field, and show how to construct its Lagrangian. Next, we develop the Lagrangian formalism for electromagnetic fields and derive the resulting equations of motion. We also examine the concept of Lorentz invariance and how it guides the construction of more sophisticated field theories. From there, we present an important discussion of Noether’s theorem and its role in identifying conserved quantities associated with symmetries. Finally, we turn to the Hamiltonian formalism for continuous fields and derive the corresponding Hamilton’s equations of motion using functional methods.