Fascinating developments in optical pulse engineering over the last 20 years lead to the generation of laser pulses as short as few femtosecond, providing a unique tool for high resolution time domain spectroscopy. However, a number of the processes in nature evolve with characteristic times of the order of 1 fs or even shorter. Time domain studies of such processes require at first place sub-fs resolution, offered by pulse depicting attosecond localisation. The generation, characterisation and proof of principle applications of such pulses is the target of the attoscience. In this book the interaction of the attosecond laser pulses with matter is investigated. The Proca's termal equation for laster - matter interaction is formulated and solved. It is shown that for attosecond laster pulses the Proca's thermal equation can be simplified and thermal Klein-Gordon equation is obtained. The book is divided into six chapters and the Epilogue presents the contemporary status of the attoscience: sub-femtosecond laster-matter interactions, master equations: Proca and Klein-Gordon equations and the perspectives: Attosecond Free Electron Laser (AFEL), LASETRON and Entangled Photon Laser (EPL).