The goal of the book is to bring together the work of researchers and practitioners working on interval methods and their applications, in the broader sense. The book also presents a the state-of-the-art in this area and fostering cross-fertilization between different approaches. It corresponds to the contributions presented at the SWIM 2014 workshop which is built on the success of previous editions, held in Montpellier in 2008, Lausanne in 2009, Nantes in 2010, Bourges in 2011,Oldenburg in 2012, and Brest in 2013. SWIM was initiated by the French MEA working group on Set Computation and Interval Techniques of the French research group on Automatic Control GDR MACS. The MEA group aims at promoting interval analysis, constraint propagation and other set methods to apply them in estimation, robotics, control, planning, design, verification, computer aided proof, and other engineering, computer science and applied mathematics areas. During previous editions of SWIM, talks were given by speakers coming from several countries among which are Brazil, Canada, France, Germany, Poland, Spain, Sweden, and Switzerland. The participants discuss their most recent ideas and developments as well as thoughts about the most promising new directions.