In vitro cultured neuronal networks coupled to microelectrode arrays (MEAs) constitute a valuable experimental model for studying changes in the neuronal dynamics at different stages of development. After a few days in culture, neurons start to connect each other with functionally active synapses, forming a random network and displaying spontaneous electrophysiological activity. The patterns of collective rhythmic activity change in time spontaneously during in vitro development. Such activity-dependent modifications play a key role in the maturation of the network and reflect changes in the synaptic efficacy, fact widely recognized as a cellular basis of learning, memory and developmental plasticity. Getting advantage from the possibilities offered by the MEAs, the aim of our study is to analyze and characterize the natural changes in dynamics of the electrophysiological activity at different ages of the culture, identifying peculiar steps of the spontaneous evolution of the network. The main finding is that between the second and the third week of culture, the network completely changes its electrophysiological patterns, both in terms of spiking and bursting activity and in terms of cross-correlation between pairs of active channels. Then the maturation process can be characterized by two main phases: modulation and shaping in the synaptic functional connectivity of the network (within the first and second week) and general moderate correlated activity, spread over the entire network, with connections properly formed and stabilized (within the fourth and fifth week).