Abstract: There are a lot of problems in physic which will finally lead to linear system problems. Theoretically solving linear system is quite simple. We can apply gauss elimination to do an Order 3 elimination work. However, practically we never solve the linear system by ourselves while the dimension is higher then 8. In this pre-colloquium we will show how the computer solve the linear system and what is different between the answer from the computer and the answer you compute by yourself. We will introduce the basic direct method and the basic iterative method and focus on "Multifrontal" which is a sparse direct method we are now working on.