We present a systematic way to consider integrable deformations
of the AdS5×S5 superstring. It is based on classical r-matrices satisfying classical Yang-Baxter equation (CYBE). Then a classical r-matrix gives rise 
to a gravitational solution that describes a deformed AdS5×S5 geometry.
In this seminar, we provide some examples including
the Lunin-Maldacena backgrounds for beta deformations of N=4 super Yang-Mills,
the Maldacena-Russo backgrounds for non-commutative gauge theories,
and Schrodinger spacetimes dual for cold atoms.
We present a systematic way to consider integrable deformations
of the AdS5×S5 superstring. It is based on classical r-matrices satisfying classical Yang-Baxter equation (CYBE). Then a classical r-matrix gives rise 
to a gravitational solution that describes a deformed AdS5×S5 geometry.
In this seminar, we provide some examples including
the Lunin-Maldacena backgrounds for beta deformations of N=4 super Yang-Mills,
the Maldacena-Russo backgrounds for non-commutative gauge theories,
and Schrodinger spacetimes dual for cold atoms.