Aqueous ink composition and urethane resin composition for aqueous ink composition

An ink set comprising a first black ink composition comprising water, a water-soluble polyurethane resin and carbon black, wherein the content of the carbon black is not less than 0.4% by weight and less than 1.5% by weight, and the content of solid matter of the water-soluble polyurethane resin is not less than 0.2% by weight and not more than 4% by weight, wherein the ink set contains a second black ink composition comprising a water-soluble polyurethane resin, water and carbon black, wherein the content of the carbon black of the second black ink composition is less than 0.4% by weight, and a content of a solid matter of the water-soluble polyurethane resin of the second black ink composition is not less than 1% by weight and not more than 10% by weight, wherein the solid matter of the water-soluble polyurethane resin of the second black ink composition is at least 7.5-fold the content of the carbon black of the second black ink composition, wherein the solid matter of the water-soluble polyurethane resin of the second black ink composition is 2-fold or more the solid matter of the water-soluble polyurethane resin of the first black ink composition.