Humans are never satisfied with what has been accomplished. There is always a desire to extend the horizons of knowledge even farther. To satisfy the scientific curiosity, as well as to push our civilization forward by investigating new physics phenomena, we need to continue improving the devices at our disposal, including high energy particle accelerators. To pave a road for a new accelerator development, beam characterization needs to be undertaken including studies of the properties of low emittance electron beams produced by laser pulses incident onto an rf gun photocathode such as described in this book. The experimental results discussed here were carried out at the A0 photoinjector at Fermilab. Such beam studies are especially important for fixing the design of new linear colliders as well as for the development of free electron lasers.