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This thesis is mainly devoted to studying integrable deformations of the${\rm AdS}_5 \times {\rm S}^5$ superstring and generalized supergravity. Westart to give a brief review of the ${\rm AdS}_5 \times {\rm S}^5$ superstringformulated in the Green-Schwartz formalism, and then introduce homogeneousYang-Baxter (YB) deformation of the ${\rm AdS}_5 \times {\rm S}^5$ superstringbased on $r$-matrices which are solutions to the homogeneous classical YBequation. By performing a supercoset construction, we derive the generalformula for homogeneous YB deformed backgrounds associated with bosonic$r$-matrices. The deformed backgrounds are shown to be solutions of thestandard type IIB supergravity or generalized supergravity. Next, we explainthat homogeneous YB deformation can be regarded as a kind of the $O(d,d)$duality transformations. Once YB deformations are realized as dualitytransformations, the corresponding $O(d,d)$ transformations are applied toalmost all backgrounds. Moreover, we discuss spacetime structures ofhomogeneous YB deformed backgrounds and clarify a T-fold structure of them byshowing the associated $O(d,d; \mathbb{Z})$ $T$-duality monodromy. Finally, weconsider the Weyl invariance of string theories in generalized supergravitybackgrounds. We show that generalized supergravity can be reproduced fromdouble field theory with the dilaton depending on a linear dual coordinate.From this result, we construct a possible counterterm to cancel out the Weylanomaly of bosonic string theories on generalized supergravity backgrounds. Inparticular, we show that the counterterm is definitely local. In this sense,string theories can be consistently defined in generalized supergravitybackgrounds.

Integrable deformations of string sigma models and generalized supergravity