Masonry structures – collections of individual solid blocks with dry or mortared contacts – appear everywhere around us, from architectural heritage through historic or contemporary civilian buildings to traffic infrastructure. The assessment of their structural integrity poses serious challenges: due to their discrete built-up, usual continuum-based calculation methods are often incapable to reflect the mechanical behavior. In cases when the failure is caused by some kind of a local effect (cracks opening up between voussoirs, individual blocks sliding out etc.) the mechanics of the problem may better be captured by methods that consider the structure as a collection of discrete bodies. Such methods are available in a wide variety today. The aim of the course is to give a detailed introduction to their theoretical fundaments, advantages and preferable fields of application, but also calling the attention to their limitations and disadvantages so that the participants of the course would build up a critical view of the choices they have when attacking a masonry mechanics problem. An explicit aim of the course is to give a sound basis for the participants to become able to develop their own methods, inspired either by classical graphical statics, or by any modern technique they find promising. The course will focus on four main topics: 1) Computerized graphical statics methods Graphical statics seemed to lose practical importance in the 2nd half of the XXth century when continuum-based numerical techniques and Limit State Analysis methods became widely applied in computerized manners. However, the recent decades brought a renaissance to the application of graphical statics in masonry analysis: powerful computer codes have been developed part of which are commercially available and part of which can be found as research tools. 2) Discrete element methods DEM was born at the end of the 1960ies as an alternative to FEM. DEM considers the simulated material or structure not as a continuum but as a collection of separate bodies being able to detach, slide, partly or completely separate, and form new contacts when large displacements may lead to the rearrangement of contact topology. Possibilities to partial cracking and sliding makes DEM particularly advantageous for masonry failure problems. 3) Blocky models The main drawback of DEM is that the analysis of whether new contacts are born in the system, simulations can be very computationally expensive. To avoid this, different blocky models have been suggested recently for problems when rearrangements of the topology are not expected, but the discrete built-up of the system is relevant (e.g. formation of partial cracks). These novel methods are considered as being in-between FEM and DEM. 4) Discrete dynamics Masonry structures are sensitive to earthquakes: seismic analysis is a crucial issue in masonry mechanics. Damping and contact sliding are significant in their energy dissipation and in the ability to adjust to ground displacements. Hence, special lectures will be devoted to the dynamics of masonry structures. In particular, lectures will focus on damping and large displacement dynamics which characterize the dynamic collapse of masonry structures. Targeted audience: young researchers (including PhD students); engineers interested in high-level computational tools for masonry analysis.