Attosecond Science - Extreme Non-Linear Optics on Ultrafast Time Scales Mette Gaarde Lund Institute of Technology, Sweden In the past six months, articles in Nature and Science have documented that two experimental groups have generated and measured pulses of coherent, extreme ultraviolet radiation with durations of a few hundred attoseconds (1000 attoseconds = 1 femtosecond). This presents a real breakthrough after almost a decade of concentrated effort in this field. Such ultrashort pulses in principle enable time resolving for instance the dynamics of electrons within atoms. I will discuss the basis for attosecond pulse generation, using high order harmonics generated in the interaction between rare gas atoms and an intense laser pulse. I will also give an introduction to high harmonic generation, and show some recent theoretical results on optimizing the harmonic radiation towards the production of as pulses, using a genetic algorithm.