Since the ribbed band is stretchy, it should fit most heads. You can adjust, of course, by making it bigger or smaller. The number of stitches should always be divisible by 8, and then you go from there.

You need ca. 200 yards of worsted weight yarn cotton. The yarn should be a little bit stiff; if it’s too soft, the hat will be limp and won’t sit right!
You can knit with four needles or with magic loop technique (which is what I do). You want to create a really tight fabric. It’s a little awkward, kind of like knitting rope, but it is needed for the finished hat!

Cast on 88 stitches. Close to the round (I usually do a few rows before closing to the round to avoid twisting; I close that little gap later with a few stitches when I weave in ends).
Round 1: purl
Round 2: knit
Round 3: knit
Round 4: knit

Round 5: knit 9, knit 2 tog, repeat throughout the round = 80 sts.

Round 6: knit
Round 7: knit
Round 8: knit

Round 9: knit 8, knit 2tog, repeat throughout the round = 72 sts.

Rounds 10, 11, 12, 13, 14, 15:
knit 1, going through back of stitch, purl1 repeat all round

Round 16: knit all stitches
Round 17: knit 9, make 1, repeat = 80 sts.
Round 18: knit all stitches
Round 19: knit 10, make 1 repeat = 88 stitches
Round 20: knit all stitches
Round 21: knit 11, make 1 repeat = 96 stitches
Round 22: knit all stitches
Round 23: knit 12, make 1 repeat = 104 stitches
Round 24: knit all stitches
Round 25: knit 13, make 1 repeat = 112 stitches
Round 26: knit all stitches
Round 27: knit 14, make 1 repeat = 120 stitches
Round 28: knit all stitches
Round 29: knit 15, make 1 repeat = 128 stitches
Round 30 knit all stitches
Round 31: knit 16, make 1 repeat = 136 stitches
Round 32: knit all stitches
Round 33: knit 17, make 1 repeat = 144 stitches
Round 34: PURL ALL STITCHES
Round 35: knit 16, knit 2 tog., repeat throughout the round
Round 36: knit all stitches
Round 37: knit 15, knit 2 tog, repeat throughout the round
Round 38: knit all stitches
Round 39: knit 14, knit 2 tog, repeat throughout the round

Continue this way, always knitting 2 tog. In the same place every other round. When you have 8 stitches left, cut the yarn, and, with a sewing needle, thread it through those 8 stitches. Pull tight, pull the yarn inside the hat and weave it in carefully. Weave in all other ends.

Soak the hat in a sink or the washing machine. Press the water out carefully. It is blocked by drying over a plate. Ideally, the edge of the plate is where the purled round is. Put the plate with the hat pulled over it on top of a a can or vase and let dry overnight. Done.