Complexity science deals with the offspring, or emergence, of large scale order and structure, in open, non-equilibrium sys- tems. Unexpected and unpredicted order can emerge from simple interactions among myriads of individuals, or degrees of freedom. Phase transitions and their implied criticality give rise to natural phenomena and properties that form a new, higher level of order which can not be deduced from the properties at the microscopic level. Examples range from the emergence of space and time in the cosmological evolution, to the evolution of the biosphere, to economic growth, or consciousness. One may seek for a new kind of natural laws governing dynamical systems of nature. The event adresses itself to the scientific community – from graduate students to senior scientists.