  This is a write-up of two lectures delivered at COST CA18108 First Training
School. They cover the motivations and some basic technical results in the
field of Doubly Special Relativity and Relative Locality. The energy-dependent
speed of light is a recurring theme here. The soccer ball problem is also
briefly described. The video recording of these and other lectures can be found
at https://www.youtube.com/channel/UChRfzgjTkO9sOkwq358kHZw/videos.
