Abu-Lughod, Janet. Before European Hegemony: The World System A.D. 1250-1350. Oxford: OUP, 1989: had been published more than 30 years ago, but this conveniently covers some essential aspects of the interaction across Eurasia OP supposedly need to know, such as commercial connections among different sub-blocks across Eurasia.
The excerpt of Francesco Balducci Pegolotti's Practical manual of Commerce (1340s) on the travel of Italian merchants on the steppes in English can also be found below:
https://depts.washington.edu/silkroad/texts/pegol.html
In addition to the basic works listed below, some introductory knowledge on Ibn Battuta's travel might also be very useful to your research, since he mainly took a visit and stayed in the Eastern Mediterranean as well as in the Golden Horde from the 1320s and 1330s:
https://orias.berkeley.edu/resources-teachers/travels-ibn-battuta
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(Entry Level)
- [Added]: King, Charles. The Black Sea: A History. Oxford: OUP, 2004, Chap. 3: illustrates the historical significance of the Black Sea region and its mouth, the Byzantine Empire, in the 13th century, in the context of acute political as well as economic rivalry between/ among the rising Italian cities, namely Venice and Genoa (and Pisa).
- Larner, John. Marco Polo and the Discovery of the World. New Haven: Yale UP, 1999: is the standard companion to Marco Polo.
- May, Timothy. The Mongols. Leeds: Arc Humanities Press, 2019. Accessed July 19, 2021. doi:10.2307/j.ctvmd838h. : is one of the two compact introductory books on the Mongols and their significance in global history. While the book itself includes the basic timeline of events and excellent further readings section, I prefer the same author's Mongol Empire (2018: see below) to this one .
- Rossabi, Morris. The Mongols: A Very Short Introduction. Oxford, 2012: is the balanced overview of the Mongols (main focus: Yuan China), including the art and cultural history. I suppose the book alone would mostly serve the purpose to update different information provided in Before European Hegemony, but it is really a shame that this introductory overview includes neither the majority of the Mongol rulers in the 14th century nor the basic timeline of the important events.
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(Intermediate Level)
- The updated easy academic readings of Italian merchants' activity in the Black Sea as well as in the Eastern Mediterranean are difficult choices, to be honest, though there are several good introductory books on Venice. While Steven A. Epstein, An Economic and Social History of Later Medieval Europe, 1000-1500, Cambridge: Cambridge UP, 2009 is certainly not without problems, it is at least better than Lopez's dated Commercial Revolution of the Middle Ages, 950-1350 (1971), and he is specialized in medieval Genoa. Anyway, Abu-Lughod (1989) at least writes some decent chapters on their activity.
- Allsen, Thomas T. Culture and Conquest in Mongol Eurasia. Cambridge: Cambridge UP, 2001: is the more detailed classic of Rossabi's Very Short Introduction, focusing on the possible contribution of the Mongol Empire in interaction of the intellectual as well as cultural ideas.
- Favereau, Marie. The Horde: How the Mongols changed the World. New Haven: Yale UP, 2021: This latest book is actually not on the Mongol Empire itself, but on the Golden Horde in the global history context, including the changing relationship among the Golden Horde, the Ilkhanate, Mamluk Egypt, and Italian merchants visiting in the Black Sea region. The majority of the works on medieval Black Sea trade tend to be of highly academic nature as well as very expensive, so this book is the very welcoming addition as a new overview work.
- Jackson, Peter. The Mongols and the West. Longman: Harlow, 2005; 2nd ed. 2017: is the basic academic overview of the relationship between the Mongols and the Europeans.
- May, Timothy. The Mongol Empire. Edinburgh: Edinburgh, 2018. The Edinburgh History of the Islamic Empires: While I can say this book is flawless in every aspect, it is at least the most standard work the whole Mongol Empire from Yuan China to the Golden Horde, including extensive lists of rulers, special word lists in Mongolian, and basic timelines as well. So, I strongly recommend this one among the intermediate level books to OP.
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Concerning Mamluk Egypt, my previous listing as well as tips in the following post might also be useful: Do you know any books about Mamluk dynasty?