The objective of this proposal is to study CAT(0) cube complexes and simplicially non-positively curved (SNPC) complexes, groups acting geometrically on them and relations between the two classes of spaces and groups. Part of the project is to study boundaries of the mentioned spaces and groups. This includes extending some results obtained by me earlier.I also plan to study the difference between groups acting geometrically on CAT(0) cube complexes and those acting on SNPC complexes. On the other hand, I will look for a theory unifying those two worlds. The host institution is Uniwersytet Wroclawski. I will be mainly working with Jacek Swiatkowski. We both have some experience in SNPC and I want to use the experience concerning CAT(0) cube complexes that I gained during my fellowship in Paris.Moreover, I will benefit a lot by working with other members of the geometric group theory team in Wroclaw which is the biggest one in Poland in the domain. I worked with some of them and I hope that the things I learned in Paris will help to increase the level of the group. One of the aims of this project is also developing the collaboration between the geometric group theory groups in Wroclaw and in Paris.Such a collaboration was started by Swiatkowski and Frederic Haglund (Orsay) and is still going on. In particular, I intend to continue our joint work with F. Haglund (Combinatorial cross-ratio on the boundary of CAT(0) cube complexes) that has begun during my fellowship in Paris. Moreover, the fellowship will prepare me excellently for a permanent academic position.