x.1 Introduction Conservation of cultural heritage buildings is a demand from society, which recognizes this heritage as a part of their identity, but it is also an economical issue. In Europe, tourism accounts for 10% of the GDP and 12% of the employment, if linked sectors are considered [x.1]. The EU is the world's number one tourist destination, with 40 % of arrivals in the world and with 7 European countries among the top ten [x.2]. According to the WTO estimates, international tourist arrivals in Europe will increase significantly. The built European heritage, namely monuments or historical centres, is a main attractor for tourism, with 45% of the UNESCO World Heritage sites within the EU. Therefore, the need for their conservation is unquestionable. Cultural heritage buildings are particularly vulnerable to disasters because they are deteriorated and damaged, they were built with materials with low resistance, they are heavy and the connections between the various structural components are often insufficient. The main causes for damage are the lack of maintenance and water-induced deterioration (from rain or rising damp), soil settlements and extreme events such as earthquakes, but there are many other causes of damage, namely: high stresses due to gravity loading, alterations in layout or construction, cyclic environmental actions, climate change, physical attack from wind and water, chemical and biological attack, vegetation growth, fire, floods, vibration and micro-tremors, and anthropogenic actions. Still, extreme events often lead to disasters, in light of the high vulnerability. A disaster is an event caused by nature or man that causes great physical damage, destruction or loss of life, or a drastic change in the natural environment. Danger is the level of threat to life, property or environment, but it is important to understand that danger is not correlated to damage, and that disasters are the result of poor risk management. Risk management involves, first, the perception and communication of risk to society. It is then essential to have proper tools for assessment and diagnosis, but also to define a set of possible solutions, and their costs, to implement a risk mitigation strategy. Over the past 30 years, economic losses due to disasters have increased tenfold, while earthquakes caused 80,000 deaths / year in the last decade (Figure 1). Studies indicate that investment in mitigation provides society an average of four times the amount invested [x.3]. In addition to savings to society, the US Federal Treasury can redirect an average of 3.65 times the money spent on mitigation resulting from disaster relief costs and tax losses avoided. This result was published in December 2005 in a report prepared by the Multi-hazard Mitigation Council of the National Institute of Building Sciences, called "Natural Hazard Mitigation Saves" [x.4]. The report was the culmination of a 3-year, Congressionally-mandated independent study. Another interesting example is given by the World Bank [x.5] and United Nations ...