This book constitutesthe refereed proceedings of theFirst International Workshop on Quantum Technology and Optimization Problems, QTOP 2019, held in Munich, Germany, in March [url] 18 full papers presented together with 1 keynote paper in this volume were carefully reviewed and selected from 21 submissions. The papers are grouped in the following topical sections: analysis of optimization problems; quantumgate algorithms; applications of quantum annealing; and foundations and quantum technologies.