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In this introductory chapter our aim is to set the scene for the following four chapters and situate them within the broad picture of mathematics education research concerning transitions. What kinds of transitions have been considered by mathematics education research? What research questions were studied and which theoretical approaches and associated methods were used? Did the studies lead to the identification of continuous processes, successive steps, or discontinuities? Are difficulties attached to the discontinuities identified, and does the research propose means to reduce those difficulties in order to foster a transition? These are the questions we study in this short literature review.