Abstract: This thesis aims to study nonlocal Lagrangians with a finite and an infinite number of degrees of freedom. We obtain an extension of Noether’s theorem and Noether’s identities for such Lagrangians. We then set up a Hamiltonian formalism for them. Furthermore, we show that rth-order Lagrangians can be treated as a particular case, and the expected results are recovered. Finally, the method developed is applied to different examples: nonlocal harmonic oscillator, p-adic particle, p-adic open string field, and electrodynamics of dispersive media.