Title: Explicit methods for hyperelliptic curves
 
Abstract: While there is much known of the theory of hyperelliptic curves in principle, explicit methods and practical implementations have been developed only beginning in the nineties starting with curves of genus 2. The case of genus 3 is much more recent and little is known for even higher genus. In this talk I want to give an overview over different explicit techniques developed, their requirements to be put in practice and some of my work regarding the genus 4 case.