Superconductivity has not only fundamental impact on condensed matter physics, but also strong potential for applications. The 2015 Gordon Conference on Superconductivity will present the cutting-edge developments in this fascinating field and will chiefly focus on unconventional superconductivity. The conference will lead to in-depth discussions on the exploration of novel superconducting materials, including cuprates, iron based superconductors, heavy-fermion, and other superconductors. For the cuprates, the emphasis will be on precursors to superconductivity, charge order in the pseudogap state, and the role of Mott physics. For iron superconductors, the emphasis will be on the pairing mechanism, the gap symmetry, and the nematic order. The conference will discuss a number of hot issues concerning unconventional superconductivity, on which no consensus has been reached yet. These include the role of spin-fluctuation pairing mechanism, quantum criticality, interface superconductivity, topological superconductivity, etc. This will be a focused, content-rich workshop on modern approaches to superconductivity in the second decade of 21st century.