Decentralization is a feature of a network. A network is made of nodes and the nature of the network is expressed by how these nodes are connected in mathematics, studied by topology. The connectedness of these nodes can be structured as centralized, or decentralized and distributed. There are quite good illustrations, about this aspect. In particular, decentralized networks are those where the connections do not refer to a single point or a very small number of nodes in the network, with respect to the total number of nodes. Decentralized networks are the basis of many different phenomena. We see networks everywhere, which is natural because when we look at certain units, the relationships between these units define networks. If we analyze the nature of these networks, from a topological point of view, we will discover that decentralized networks are all over the place. Let me start with just two examples. The universe itself is a decentralized network. Look at hydrogen, created in the Big Bang, and expanding under the influence of the various fundamental forces, attracted and becoming ever more clumpy due to gravity, to the point where it starts forming stars, the stars starting to aggregate into galaxies. All of that is happening everywhere, without any kind of central coordination, due to laws that are universally applicable. Another example is biology. The cells in your body form a very complex, and well functioning network. There are cells of many kinds, and the functioning of most of these cells is coordinated as they communicate. They act in a manner that benefits the entire organism, that benefits you. However, the cells are able to carry out most of these activities without any kind of central coordination.They react and they activate certain types of metabolic activities based on local phenomena, chemical influences, the arrival of certain types of proteins or messenger RNA. But they don't need a central system to tell the cells what to do. A third example is in the way that many pieces of the economy work. In a capitalist society, it is assumed that each actor in the economy can make decisions on their own, independently of each other. There is no central planning, and no one imposes on the single actors in the economy, what they should do, or they shouldn't do, what kind of product or service they should provide. It is the sum of their decisions that creates what we call the market. The market arrives at a certain consensus, at a certain balance of these decisions, that are formed by all the actors together. Once again, without the central coordination. During this course we are going to highlight. Many technological, economical, even political forces that are leading towards decentralization. But the value judgment, whether decentralization is better, is actually different and independent. Sometimes, even the question is not necessarily applicable, a different form of the question is, which solution in the particular topology of the network is fit to the particular evolutionary niche that it should dynamically live within. In the cases that we will illustrate decentralized solutions can be fitter than centralized solutions. Another way of asking the question is whether a decentralized network is always more efficient than a centralized network. And it may be surprising, but the answer to this is almost always no: a decentralized network will be less efficient. If you think about it, it is easy to realize why. A decentralized network will unavoidably contain redundancies and replications of functions that a centralized network doesn't need to have, because it can select and take control of those functions that are vital to the working of the network. While in the decentralized solution each of those functions must be present locally everywhere where the network has to operate. It cannot be in just some places. So by definition a decentralized network is less efficient than a centralized one. However, the fitness function may not maximize efficiency. It may maximize other kinds of needs, such as resilience, and the decentralized network is almost always more resilient than a centralized one.