We report guiding and manipulation of charged particle beams by means of electrostatic optics based on a principle similar to the electrodynamic Paul trap. We use hundreds of electrodes fabricated on planar substrates and supplied with static voltages to create a ponderomotive potential for charged particles in motion. Shape and strength of the potential can be locally tailored by the electrodes layout and the applied voltages, enabling the control of charged particle beams within precisely engineered effective potentials. We demonstrate guiding of electrons and ions for a large range of energies (from 20 to 5000 eV) and masses (5E-4 to 131 atomic mass units) as well as electron beam splitting as a proof-of-concept for more complex beam manipulation. Simultaneous confinement of charged particles with different masses is possible, as well as guiding of electrons with energies in the keV regime, and the creation of highly customizable potential landscapes, which is all hard to impossible with conventional electrodynamic Paul traps.