There are as many as 80 galaxies in our local group; most of them are small and satellites of the 3 major players - The Milky Way, Andromeda and Triangulum. This is the Triangulum galaxy, the smallest of the big three in our group.

Both Andromeda and Triangulum are closing in on the Milky way. Andromeda is closer at 2.5 million light years, closing in at 110 km/sec, while Triangulum, though slightly farther away at 2.73 million light years, is moving faster at 190 km/sec in our direction. Within the errors of measurement, both will get here at the same time - if they hit us at all. It's hard to measure the trajectory of something coming at you, and these galaxies might well miss us completely. The 3 galaxies will not be able to avoid an intense gravitational interaction, which will be seen as flows of gas and stars streaming in all directions, but the galaxies may not enter into each other "personal space". Even if they do it's unlikely that there will be stars bouncing around like billiard balls - there's just too much empty space in a galaxy. If anyone is left to make notes, the starlit skies will become amazingly bright!