In Kati of Terra Book 2: On Assignment to the Planet of the Exalted, Kati discovers that she hasn’t just been kidnapped to a location few star systems from Earth, but has, in fact, travelled a lot farther:
Lienel r’pa Gradin had frozen the image at a point where Katie-who-once-was, had been examining a representation of the galaxy. There it had been, filling most of the large, glossy page, with its countless stars forming a spiral shape with the two arms extending out, and a black arrow pointing to the approximate location of the sun around which Kati’s home world orbited.
“Perhaps you are not aware—and there is no reason why you would be, unless someone had happened to mention it—that the World Lamania and its sun are not in a spiral galaxy. We of the Star Federation know of them, of course, and have known, for a long, long time, but we do not, in fact, live in one. Our galaxy has a more amorphous shape; it lacks the beautiful symmetry of the spiral galaxies.”
Kati’s head had swum; then the granda had come to her aid, and worked on her nervous system to allow her to regain some equilibrium.
“Are you saying,” she had asked, “that I have—somehow—travelled right out of my galaxy and into another one?”
There are many complex classification schemes for galaxies, but the main distinctions are between spiral, elliptical and lenticular galaxies. Our solar system lies within the Milky Way galaxy, thought to be a barred spiral galaxy. The Andromeda galaxy, easily seen through a small telescope, is another prominent spiral galaxy. Most people would agree with Lienel r’pa Gradin that spiral galaxies are indeed very beautiful. Elliptical galaxies, similar to the one that Kati now finds herself in, are ellipsoid shaped, more or less what we would call egg or football shaped, and therefore not nearly as visually striking. A famous example of an elliptical is the satellite galaxy of Andromeda, known as M32. M87 in the Virgo cluster (also visible in a small telescope in a dark sky) is another well-known example.
At one time it was thought that spiral galaxies eventually evolved into elliptical galaxies, but that is evidently not true, as the stars in elliptical galaxies tend to be older on average than those in spiral galaxies, and they seem to have lower rates of star formation. Maybe that explains the profusion of intelligent life in Kati’s new galaxy, compared to our own i.e. there has simply had more time for intelligence to involve and spread in that galaxy
Lenticular galaxies are intermediate between spirals and ellipticals, similar to spirals in having disks, but lacking spiral arms. They also have relatively old stars and relatively low star formation rates.
One interesting theory concerning the shapes of galaxies involves collisions between galaxies and the resulting mergers. This seems like a fantastic idea, but modelling shows that for the most part the galaxies involved would pass through each other, with no actual stellar collisions. However, these events could affect the shape of the resulting merged galaxy, and also trigger episodes of enhanced star formation. The remarkable Cartwheel galaxy is thought to be a result of such a cosmic collision.