Hej,
I
will explain here the basic technique to make a european 4 in 1
chainmail coif. I used 10mm rings made with 1.8mm wire here.
That
technique is commonly known as "expanding circle".
Making the top-of-the-head
circle :
To fit the top of the head, we need a circle. We
start it by passing 8 rings through one :
(click to enlarge)

We add
16 rings to that. Those are the 8 "normal" 4 in 1 rings, plus one more
extra ring through each 8 rings of the first pic :
(click to
enlarge, the green spots show the normal 4 in 1 rings, and the red spot
show the extra ring)

On
that picture, the next
rings are already added, they are normal 4 in 1 rings passing through 2
other rings. We still have 16 rings.
(click to enlarge, the
green spots show the normal 4 in 1 rings, and the red spots show the
extra rings)

Next
step is just adding 16 more rings :

We
increase the number of rings just as we did in step 2, by adding 1 ring
between each of the 16 external rings, we now have 32 external
rings :
(click to enlarge, the green spots show the 16
external rings of the previous picture, and the red spots show the
extra rings)

Now
we will add a 4 in 1 chain, no increasing at all (still 32 external
rings) :

Here
is the result, we have a nice circle already, but not quite wide enough
yet :

At
this step we increase the number again to reach 64 external rings. Just
as we did in the previous steps, we add one extra ring between each
external ring :

Just
one more step, we add another 4 in 1 chain :

Here
is the circle, which should be large enough for most heads (it should
reach your eyebrows, if not just add one chain) :

Covering the whole head :
That circle we have doesn't cover much yet, but the important part is
done,
since the part from that to the bottom of the head is just a 4 in 1
sheet, with a hole for the eyes and the nose.
Once
you have reached the shoulders, increase again the number of rings on one
line, and continue a few more standart 4 in 1 to make the mantle.