I guess that Granny Squares are the first REAL project for the many beginner crocheters. First off all, it looks like a FINISHED project by itself. (I've done myself!) Secondly, it presents you to the countless opportunities for creativity. Sew or crochet them together and here you are: Afghans, blankets, stoles and scarves, ponchos and vests, end etc.
Is it too boring for you to crochet only rectangular using Granny's? Just be a little bit creative and you can do more complicated projects: skirts and sweaters, tunics and cardigans, coats and whatever you wish.
The only "problem" I can see here is too many variations available for the crocheting Granny's. :) Let's begin from the simplest one a Solid Granny Square.

I used it to design a Crochet Slipper Pattern. My grandma used to crochet them for the whole family.
The main thing crocheting in crocheting a square is to keep it flat. Since a square is worked in rounds, you begin in the center of a square and your square grows outward.
To keep a square flat, a certain number of increases is required per each row. A number of increases can be calculated by the "Law of a Square". Here, is the theory, which works for any type of stitches you use to crochet a square. According to this law (see the picture below) :-)

To practice, follow a video below which demonstrates how to crochet a solid Granny Squares if you use a double crochet stitch. The main thing for you to remember is the number of increases required per each row. To form every corner, you crochet two chains for each of them (2 x 4 = 8 total per row.)
If you are the beginner in crocheting, follow the link below. These videos would be very helpful for you. They demonstrate a very detailed explanation about crocheting Granny Square with double crochet stitches.
Now it is time for more serious project. A Crochet Slipper Pattern project is a good start. It has at least three attractive moments: easy to crochet (Granny squares only!), looks quite decent, a thing which will always be handy and appreciated as a gift.
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