Here, we report on the working group ''Optics and Beam Transport'' of the 2005 Energy-Recovery-Linac Workshop. This workshop also had working groups on ''Electron Guns and Injector Designs'', ''Superconducting RF and RF Control'', and ''Synchronization and Diagnostics/Instrumentation''. Here, we are concerned with the many different ERL proposals that international laboratories have been working on. Subjects of concern are optics, accelerator design and modeling, stability requirements, designs of the merger that connects the conventional injector linac with the Energy Recovery Linac, longitudinal phase space manipulations to produce short pulses, beam dynamics and limitations by beam instabilities, and computational aspects of space-charge and synchrotron radiation effects. A coarse grain overview is given and reference is made to more detailed articles that were presented in this working group. Subjects are identified where collaborations should be encouraged and areas of future R&D are prioritized.