  In this dissertation we study hidden symmetries within the framework of
string theory. There are two kinds of hidden symmetries investigated in this
work: the first type is associated with dynamics of quantum fields and the
second type is related to integrability of strings on various backgrounds. The
goals of this thesis are twofold: extension of hidden symmetries known in
general relativity to stringy backgrounds in higher dimensions and construction
of new integrable string theories.
  In the context of the first goal we study hidden symmetries of stringy
backgrounds, with and without supersymmetry. For supersymmetric geometries
produced by D--branes we identify the backgrounds with solvable equations for
geodesics, which can potentially give rise to integrable string theories.
Relaxing the requirement of supersymmetry, we also study charged black holes in
higher dimensions and identify their hidden symmetries encoded in so--called
Killing(-Yano) tensors. We construct the explicit form of the Killing(-Yano)
tensors for the charged rotating black hole in arbitrary number of dimensions,
study behavior of such tensors under string dualities, and use the analysis of
hidden symmetries to explain why exact solutions for black rings (black holes
with non-spherical event horizons) in more than five dimensions remain elusive.
As a byproduct we identify the standard parameterization of AdSp x S^q
backgrounds with elliptic coordinates on a flat base.
  The second goal of this work is construction of new integrable string
theories by applying continuous deformations of known examples. We use the
recent developments called (generalized) lambda-deformation to construct new
integrable backgrounds depending on several continuous parameters and study
analytical properties of the such deformations.
