Simulational studies of colliding disk galaxies are presented, using restricted three-body, hydrodynamical, and kinematic model methods. Depending on the collision parameters, two seemingly different types of disturbed galaxies arise: ring galaxies and leading one-arm spirals;Since the pioneering work of Theys and Speigel (1976) and Lynds and Toomre (1976), it is known that ring galaxies may result from a nearly head-on passage of an arbitrary galaxy through a disk galaxy, and the formation mechanism is almost a purely kinematic phenomenon. Our first research project consists of a quantitative in-depth study of the properties of ring galaxies, and their dependence on the collision parameters and the structures of the colliding galaxies;The second research project deals with effects of dynamical friction and nearly head-on multiple passages and merger on a disk galaxy. In our simulations, we find that for realistic parameters, encounters may give rise to the merger of a ring galaxy with its intruding companion. Furthermore, the multiple passages and merger generate various features in the target disk which are distinct from the structures characteristic of simulated single-passage rings. In view of these differences, a physical classification of collisional ring galaxies based on the presence of an apparent companion, as well as the morphology and kinematics of the target disk is proposed. Our proposed classification may be identified with an empirical classification of Few and Madore (1986);For a different range of collisional parameters, namely a single nearly perpendicular, off-center passage of a companion through a disk galaxy, a leading one-arm spiral is formed. In the past, only co-planar, retrograde encounters have been considered for the formation of collisional leading one-arm spirals (Thomasson et al. 1989, Athanassoula 1978). Furthermore, our simulations suggest an intimate relationship between ring galaxies, and leading one-arm spirals. The degree of off-centeredness of the perpendicular collision determines which of the two types will form;We have also developed a method for evaluating the gravitational field created by a flattened mass distribution for use in our restricted three-body code.