In order to accelerate charged particles, electric fields have to be applied. The highest electric fields reached in radio frequency particle accelerators are of the order of 10 MV/m. This field poses an upper limit for conventional accelerator technology because for higher fields the electrodes will be ionized. What if this limit is circumvented and the electric field is build up in an already ionized medium? The idea of using laser generated plasmas for particle acceleration has been conceived about 25 years ago, and is currently a very active and fascinating subject in theoretical and experimental physics. In a plasma the maximum attainable electric fields are of the order of 1000 GV/m, five orders of magnitude larger than for RF accelerators. The dimensions to generate high energy particles shrink from kilometers to millimeters. Therefore, laser plasma acceleration may become an attractive future option for particle acceleration. In this work experimental contributions to the generation of particle beams from laser plasmas are presented. Electron beams with improved parameters, and the first quasi monoenergetic proton beams have been generated and investigated utilizing a compact table top laser system at the Jena laser facility. These experiments are described and discussed in this book.