There's a very large literature, starting with one of the most important works of history of the 20th century, Fernand Braudel's "The Mediterranean and the Mediterranean World in the Age of Philip II" -- a giant work jammed with, well, everything about the period. While its an older work and massive, it's important to historians and fun to read -- if you read it more like an encyclopedia rather than attempt to plow through cover to cover.

Braudel was one of the leaders of the French Annales school of history, which was at the time a new way of writing history, a very deep concern with material life and environment, as opposed to battles, kings and dates -- these historians care a lot about trade, and a lot about technology. So it's important not just for its coverage of the subject, but as a example of [what was at the time it was written] a new way of studying and writing history.

Because Braudel is so broad, there's likely something in it that touches on almost any question you might have, certainly in the later part of your time frame -- he's got less information for the 13th and 14th centuries .

Once you've had a look at that, there are all sorts of more recent and more detailed works you can dig into-- when I say "detailed", I mean it. Archives have survived, and over the last 75 years several generations scholars have scoured them. So for example, you have all kinds of works devoted to the trade of specific cities, Genoa, Florence, Venice each have a very large literature. Even cities which might be less well known, like Livorno, have gotten the treatment.

So there are very specific works like Michael Mallet's "The Florentine Galleys in the Fifteenth Century", and there's Roger Crowley's "City of Fortune: How Venice Ruled the Seas" -- Crowley isn't an academic historian, but he writes well and does a good job of delivering a good story and a reasonably nuanced version of the story. You may prefer this to Braudel if you're looking for more of a "good read" vs more of a detailed academic work.

On trade itself, on the earlier end of your time frame, there's the wonderful "Power and Profit: The Merchant in Medieval Europe" by Peter Spufford; a handsome book, written by an expert but for a popular audience, beautifully illustrated. Perhaps more oriented to continental trade than Mediterranean, but there's a lot of everything in it. Spufford is very clear on "how trade and money worked" -- he's also useful on the way that the economic center of gravity was moving away from the Mediterranean in this period.

So: quite a few general works, and behind them a remarkable library of journal articles and dissertations digging into the most detailed of subjects. You want to know the specific schedule that a Venetian galley took, traveling East along the Adriatic to Greece? That's in Fasano-Guarini Elena. Au XVIe siècle : comment naviguent les galères. In: Annales. Economies, sociétés, civilisations. 16ᵉ année, N. 2, 1961. pp. 279-296 -- a chart of the trip is here:

https://i.redd.it/6nxee1j40du31.png

Noel Malcolm has recently dug into a little studied but relevant slice of your subject, the Albanian coast in "Agents of Empire: Knights, Corsairs, Jesuits and Spies in the Sixteenth-Century Mediterranean World" [2015]

So you can read broadly, or very specifically. If you want to study the wool trade between England and Italy-- there are detailed studies of that. If you want to study shipbuilding, there are studies of that. If you want to study naval warfare, the shelves groan under the weight of books about Lepanto, the Siege of Malta, the Venetian Navy and more.