All ribbing is a combination of knit and purl stitches across a row. When you knit back on the next row, you knit the stitches as the face you, that is, knit the knit stitches and purl the purl stitches. The knit stitches form a ridge (or rib) and the purl stitches form a valley. Ribbing is essentially a reversible fabric. Ribbing is elastic crosswise and will stretch lengthwise and is most often used for sweater neckbands and bottoms and the cuff of socks. Ribbing also “pulls in” naturally, so it will effect the shape of your garment.
One-By-One (1×1) Ribbing:
This is knitted exactly as it says. Knit 1 stitch, purl 1 stitch across the row. (Remember to move your yarn from back to front as you knit and purl.) If you are knitting this ribbing flat for a garment, you should be knitting an odd number of stitches, so that when the garment is seamed together the ribbing will appear to be continuous. If you are knitting in the round, you should always have an even number of stitches. This ribbing is the most elastic of ribbings. It tends to look more loosely knit than stockinette stitch, and because it is so elastic, most patterns have you knit your ribbing on needles that are a size or two smaller than the body of the pattern.
Two-By-Two (2×2) Ribbing:
This ribbing is made by K2, P2 across the row. It is a multiple of 4 stitches, so when knitting a flat piece to be joined with another, you should be knitting a multiple of 4 plus 1 stitch so that the pieces will weave together correctly. For knitting in the round, you would knit over a multiple of 4 stitches. This is a popular ribbing and it works well for sock cuffs, but it is not as elastic as the 1×1 ribbing.
Three-By-One (3×1) Ribbing:
This ribbing is also a multiple of 4 stitches: K3, P1 across. The rules for 2×2 ribbing also apply to this ribbing. As you can see in the picture, this produces a wide rib with an almost invisible valley. I have seen this ribbing used in sock patterns and it does give the socks and attractive looking cuff.
Other Ribbing Patterns: There are many other variations of ribbing, including Cabled Ribbing, Four-By-Two Ribbing, and Six-by-Three Ribbing. I will include an example of Cabled Ribbing in a latter post on Cable Stitch Patterns.
Note: For information about tension issues with ribbing, see my post: Master Knitter Level I – Swatches # 1, 2, & 3.
Here’s a picture of the swatch. I cast on 44 stitches so that I could have a 40 stitch area surrounded by a 2 stitch garter stitch edging. I started using US 2 (3.00 mm) needles and then switched to a smaller US 1 (2.50 mm) needle for the last part of the swatch. I did a section of garter stitch, then stockinette stitch, then the color pattern using the lighter aqua blue as the main color and then switched to using the darker teal blue as the main color. I finished the swatch by doing a section of sockinette stitch on the smaller needles, followed by a section of garter stitch. 
