First notebook entry: Introducing myself

Hello all :)
i'm Samih,from Algeria, i'm learning English,because i want go to the US to continue my studying there and look for a work.
my native languge is Berbère,and i speak very well Arabic very well languge,and well French languge well.
i study electromechanic 2nd year at university.
i enjoy to swimme,and play gymnastics gymnastique

You could have said to "look for work" or "look for a job".

I changed your second sentence to read "I speak Arabic very well", but it could also say "I speak the Arabic language very well".

In English people usually say "do gymnastics" instead of "play gymnastics".