This book constitutes the refereed proceedings of the First International Workshop on Quantum Technology and Optimization Problems, QTOP 2019, held in Munich, Germany, in March 2019. The 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; quantum gate algorithms; applications of quantum annealing; and foundations and quantum technologies.