This booklet contains the lecture notes prepared by the foreign lecturers at the DCAMM Advanced School 'Advanced Topics in Structural Optimization1 held at the Technical University of Denmark, June 25 to Juli 3, 1998. The material covered by the notes is not readily accesible in current literature as unified presentations directed towards the strucural optimization community. The purpose of this publication is thus to make the material available to a broader audience.We would like to thank the authors, Wolfgang Achtziger, Kai-Uwe Bletzinger, andKrister Svanberg for taking the time and effort in preparing their contributions and for allowing DCAMM to print their notes in the DCAMM Special Report Series.The DCAMM Advanced School 'Advanced Topics in Structural Optimization' was held under the auspices of the DCAMM International Graduate Research School in Applied Mechanics. The support received from the Danish Research Academy is gratefully acknowledged.