Electron scattering, a subset of atomic molecular physics, plays a key role in many areas of science and technology. It can be used as probes in a wide range of natural processes. This book reports electron impact collision calculations on atomic and molecular targets relevant to plasma and astrophysical systems. It covers theoretical research in these areas on the electron collision and ionization of various atomic and molecular targets in the lower and intermediate energies. We report a simple and effective method developed by our group, which provides an estimate for family of cross sections: total elastic cross sections, total inelastic cross sections, total cross section , rotational cross sections and grand total cross sections for electron scattering from atoms and molecules. The results of such calculations are compared with experiments and with other calculations. Apart from these calculations, the present book also investigates theoretical work on a molecule BF at low energies using R-matrix formulation in the Quantemol-N software. These calculations can be useful to both the experimentalists as well as theoretians in their research work.