We investigate the head-on and overtaking collision of two, two-sided double and two-sided triple solitons, in electrostatic and electromagnetic plasmas in this thesis. We considered quasi-elastic head-on collision between two oppositely propagating dust ion acoustic (DIA) solitary waves, in a nonmagnetized plasma composed of adiabatic ions, stationary dust charged concentration and inertialess kappa distributed electrons. We linearly analyse the DIA waves and derive the relation. We examined the head-on collision between two oblique opposite travelling DIA solitons in collisionless magnetized plasmas. To deduced the two sided Korteweg–de Vries (KdV) equations, their corresponding trajectories and phase shifts for unmagnetized and magnetized plasmas the the extended Poincar´e-Lighthill-Kuo (PLK) method has been used. For a critical case, we derived modified Korteweg–de Vries (mKdV) equations, trajectories and phase shifts for a negative dust charged concentration. We numerically analyse the results. By using two fluid model composed of warm electrons and cold ions we considered the interaction between two magnetoacoustic solitons. The dispersion effects appears through electron skin depth. The KdV equations and phase shifts has been derived for the two oppositely moving magnetoacoustic solitons. The head-on and overtaking collision between two, two-sided double and two-sided triple magnetoacoustic oppositely moving solitons has been reported in electron-positron plasmas. For the overtaking collision the Hirota bilinear method has been employed to derived the collision of multiple solitons. The KdV equations and phase shifts due to both collision are derived. It is found that magnetoacoustic compressive solitons are formed. The interaction of kinetic Alfv´en (KA) solitons in electron-ion low β plasma with kappa distributed electron has been examined. For the collision at an angle of 180◦, two sided KdV equations and their corresponding phase shifts has been derived under the condition of secularity. We further investigated the interaction of four and six KA solitons, it is observed that sub-Alfv´enic compressive solitons are exist.