## 2 New Frontiers  
Several frontiers in Parameterized Complexity, either new or with well-established roots, but still in their infancy, are represented in this collection. All of these frontiers go \"hand in hand\" with the overarching goal of increasing the scope and impact of Parameterized Complexity. To this end, first and foremost, parameterized algorithms should be made practical. This, of course, means that specific methods to enhance performance in practice are to be developed. Novel approaches to do so, with an emphasis on treewidth, the most well-studied width measure in the field, are given by [PERSON] et al., and by [PERSON] and [PERSON]. Further, basic machinery in Parameterized Complexity should be exported to work when the input is not a graph. Indeed, most problems in practice are not about graphs, yet some of them can be modeled by graphs. For example, Integer Linear Programming (ILP) is a ubiquitous language to formulate problems, which is used in practice, and [PERSON] and [PERSON] survey how it can be modeled by parameterized graph problems. Additionally, [PERSON] et al. do so for the kidney exchange problem. Taking a broader perspective, [PERSON] and [PERSON] survey new challenges for parameterized complexity in bioinformatics, where problems often concern entities that are not \"just\" graphs or are not graphs at all. To design practical parameterized algorithms, additional considerations are often required. Specifically, in practice, it may not be clear how to determine what the \"best\" solution is. Therefore, we might wish to compute several solutions. [PERSON] et al. present results for the enumeration of solutions with FPT delay, and [PERSON] et al. highlight diversity as a measure of the quality of a set of solutions. In addition to uncertainty with respect to the best solution, the input itself might be uncertain (in a different sense). This issue is discussed by [PERSON] and [PERSON]. Further, the paradigm of parameterized complexity by itself might not be enough, for example, when no efficient fixed-parameter algorithm, or no fixed-parameter algorithm at all, is likely to exist for some problems. In this regard, a research direction that has received growing attention in recent years is that of parameterized approximation, surveyed by [PERSON] et al., and a specific result is given by [PERSON]. Another framework to handle this is offered by SAT-solvers, which are often employed in practice, as surveyed by [PERSON] and [PERSON]. **Beyond Fixed-Parameter Tractability: New Paradigms. ** In recent years, the paradigm of Parameterized Complexity has been \"combined\" with other algorithm design paradigms, including approximation algorithms, streaming algorithms, dynamic algorithms and distributed algorithms. The last three focus on the design of parameterized algorithms that can be used under additional constraints/features of the input and the computation entities involved, such as a lack of space or the necessity to efficiently deal with small changes in the input that occur over time. Approximation algorithms, like Parameterized Complexity, is a framework to deal with computationally hard problems. Here, we compromise the \"quality\" of the solution, but still demand that the algorithm run in polynomial time. By compromising both quality and running time, we can compromise each of them by just a little bit rather than one of them by a lot. For example, we can achieve a \((1+\epsilon)\)-approximate solution in FPT time for a problem that is unlikely to admit any constant-factor approximation algorithm in polynomial time and which is W[1]-hard, and hence enjoy both. In this collection, [PERSON] et al. survey both positive algorithmic and hardness results in Parameterized Approximation. Further, [PERSON] presents a result in the context of circuits, showing negative results regarding the approximability of the Dominating Set by para-AC\({}^{0}\) circuits. Another framework to deal with problems that are computationally hard even when FPT time is allowed is to employ SAT solvers.