The 13th International Conference on Gravitation, Astrophysics and Cosmology (ICGAC-XIII) and the 15th Italian-Korean Symposium on Relativistic Astrophysics (IK15) will be jointly held at Ewha University in Seoul, Korea during July 3-7, 2017. ICGAC is the series of biennial conferences on Gravitation, Astrophysics and Cosmology which take place in the Asia-Pacific region, with the goals to promote cooperation among the member countries and within an international context, high level studies on hot topics and to encourage young physicists on these fields. This conference has been one of the key programs sponsored by APCTP over the past twenty years. It has been hosted by AP regions: Seoul, Korea (1993); Hsinchu, Taiwan (1995); Tokyo, Japan (1997); Beijing, China (1999); Moscow, Russia (2001); Seoul, Korea (2003); Jhongli, Taiwan (2005); Nara, Japan (2007); Wuhan, China (2009, webpage); Qui-Nhon, Vietnam (2011, webpage); Almaty, Kazakhstan (2013); Moscow, Russia (2015, webpage). After ICGAC-XIII (2017), it will be held in Brazil in 2020 and will be held in a sequence of MG, GRG and ICGAC for every three years. This means APCTP will sponsor one of the three main international conferences in astrophysics and cosmology. ICGAC is one of three key programs in astrophysics in the AP regions: ICGAC, CosPA and AP School on GC, which played the key role in forming the Division of Astrophysics, Cosmology and Gravitation (DACG) of AAPPS (Association of Asia Pacific Physics Society). APCTP has exchanged MOU with AAPPS and DACG will be an important partner in APCTP activities. So, it is planned that this conference will be held as a key activity of DACG, AAPPS in 2017. Italian-Korean Symposium on Relativistic Astrophysics (IK) was started at 1987, then continued for every two years alternatively in Korea and Italy with the support of Korea Science and Engineering Foundation (KOSEF), Consiglio Nazionale delle Ricerche (CNR), International Center for Relativistic Astrophysics Netwrok (ICRANet) and hosting institutes. Main purpose of this symposium is accelerating the exchange between scientists of Italy and Korea, especially for young researchers. To elaborate the interest of audience and diverge the participants, meeting in 2017 will be held jointly with The 13th International Conference on Gravitation, Astrophysics and Cosmology (ICGAC-XIII). IK meetings in the past can be found in IK14 (Pescara, Italy 2015, webpage), IK13 (Seoul, Korea 2013, webpage), IK12 (Pescara, Italy 2011, webpage), IK11 (Seoul, Korea 2009, webpage), IK10 (Pescara, Italy 2007, webpage), IK9 (Seoul & Geumgang Mountain, Korea 2005, webpage), IK8 (Rome & Pescara, Italy 2003, webpage), IK7 (Gimhae & Gangwha Island, Korea 2001, webpage), IK6 (Rome & Pescara, Italy 1999, webpage), IK5 (Seoul & Suanbo, Korea 1997), IK4 (Rome, Gran Sasso & Pescara, Italy 1995, webpage), IK3 (Seoul & Kyungju, Korea 1991), IK2 (Rome & Limone Piemonte, Italy 1989) and IK1 (Seoul & Sorak Mountain, Korea 1987). This conference is hosted by Ewha Womans University, organized by Astrophysics Division of Korea Physical Society and International Center for Relativistic Astrophysics Network, and supported by Asia Pacific Center for Theoretical Physics, Division of Astrophysics, Cosmology and Gravitation in the Association of Asia Pacific Physics Society, National Research Foundation, Consiglio Nazionale delle Ricerche (Italy), Konkuk University, Institute for Basic Science, and Kunsan National University. Topics: -Classical Gravity, GR Extensions -Classical and Quantum Cosmology -Dark Matter and Dark Energy -Black Holes, Wormholes -Strings, Branes, Higher Spin Fields and Quantum Gravity -Extra Dimensions and Variation of Constants -Experimental Studies of Gravity and Fundamental Physics Space Projects -Gravitational Waves -Numerical Relativity -Relativistic Astrophysics -White Dwarfs, Neutron Stars and Gamma Ray Bursts -And Others