Developments in theoretical physics include instances of the unification of quite different phenomena. The theoretical community is challenged by the growing interactions between high-energy physics, statistical physics, and condensed matter physics. The common language, though, is exact solutions of two-dimensional and conformable field theories. This volume is a faithful representation of this interdisciplinary domain. Conformable and integrable field theories have become an active research topic - the main developments concern the boundary effects and applications to disordered systems. The number of applications of the exact methods to condensed-matter problems has been growing over the years. At the beginning of the 21st century, it is widely recognized that strongly interacting systems in low dimensions can be successfully described by integrable and conformable theories. This volume was written to aid those seeking to find their way in this domain.