MEGA is the acronym for Effective Methods in Algebraic Geometry (and its equivalent in various languages). In this series of biennial international conferences, with the tradition dating back to 1990, MEGA 2019 was the 15th one and was held during June 17 - 21, 2019 in Madrid. The scope of effective methods in algebraic geometry is regarded in a broad sense, including their foundations, analysis, complexity, computational aspects, practical issues and applications. Through its particular format with a competitive submission process for the regular talks, the MEGA conference series facilitates to promote leading research in these fields.