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.