  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 $r^{\rm th}$-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.
