Ricci Solitons in Dimensions $4$ and Higher offers a detailed account of recent developments of Ricci solitons-self-similar solutions to the Ricci flow equation-which play a central role in modeling the formation of singularities of the flow. Building on the foundational work of Hamilton and Perelman and the recent advances of Bamler, Brendle, and others, this book focuses on the rich and technically demanding theory of these solutions. With special attention to dimension $4$-where potential applications to the topology of smooth 4-manifolds are most promising-the authors present key...