You can have a vinyl-lined pool in any shape your heart (or your imagination) desires. That being said, there are some popular shapes that you'll hear discussed more often than others. You'll notice that a single category of pool can have several variations. You'll also notice that pool shapes can be blended (the Lazy 'L' Grecian is one example). This post includes a basic illustration of the shape, and pictures of some of the variations. Once you've got the basic lingo down, you'll be better able to identify the looks you like and talk to pool installers about them.