Does anybody make electric timers which will shut off the electricity
for approximately 10 minutes, turn it on for approximately 20 minutes
and again shut it of for 10 minutes and keep repeating doing this?

Hello vaac, the key to finding what you are looking for is knowing
what to call it. After a couple of tries I found "repeat cycle timer".
Here are links to two timers that will do what you want:

http://www.automatictiming.com/pages_atc/repeatcycletimers.html#342

The 342 is a repeat cycle panel mounted timer with two separately
adjustable On and Off times. Designed with a heavy duty DPDT 7A Relay,
the 342 can cycle a load On and Off repeatedly as long as the timer is
powered. Time ranges from 50ms to 10 Hrs. are knob selectable.
Operating voltage is universal.

http://www.airotronics.com/repeatcycle/mc.htm

The MC Series repeat cycle timers use a micro processor platform to
provide excellent accuracy and repeatability. Time settings are easy
with the integral dip switches. These units can handle loads up to 20
amps (1.5 HP) without heat sinking.

Application of input voltage to the timer starts the ?On? time delay.
At the end of the ?On? time delay, the ?Off? time delay starts. At the
end of the ?Off? time delay, the load is again energized, the timer
returns to the ?On? time delay, and the cycling continues as long as
input voltage is applied. When the ?Off? time is first, the sequence
will be reversed. Removal of the input voltage resets the timer.

Here is a link to the entire product line:

http://www.airotronics.com/repeatcycle/index.htm

Hope this helps you out, Redhoss

Thank you very much, redhoss-ga, for your ansewer.