Galaxies are composed mostly of 1) gas, 2) stars/stellar-like objects and 3) dark matter. A collision between two galaxies is devastating for the gas (a shock wave is driven through the gas clouds, heating and compressing the gas which leads to star formation in colliding galaxies).
On the other hand, the stars should emerge unscathed. The typical star in a galaxy is an M dwarf, of which they are about 20 pc-2 in the solar neighborhood. The typical radius, RM of these stars is 4.4x1010 cm, which gives a fraction of the area of the galactic disk filled by the disks of these stars to be
thus, even a direct hit between galaxies means that the probability that even one of the 1013 stars would collide is quite small.
However, the distribution and dynamics of the stars would be radically changed by a collision, or near-miss, due to the deflection by the satellite galaxy's gravitational potential. Thus, began the study of colliding or interacting galaxies in the early 70's.
What started all this speculation on galaxy collisions? The Arp Atlas of Peculiar Galaxies
These unusual objects in the Arp Atlas motivated a series of studies using primitive N-body simulations (N = few 100 particles). The most famous were the Toomre and Toomre simulations (circa 1972).