We will talk about our contribution to a large project with the goal

of a self-consistent numerical simulation of the evolution of the

universe beginning soon after the Big Bang and ending with the

formation of realistic stellar systems like the Milky Way. This is a

multi-scale problem of vast proportions. It requires the development

of new numerical methods that excel in accuracy, parallel scalability

to the processes relevant in galaxy formation. These numerical methods

themselves require the development of mathematical theory in order to

guarantee the above mentioned requirements. in this talk we shall

focus on our contribution to this effort. This is joint work among

others with Volker Springel.