ON CHRISTOPHER COLUMBUS, I would recommend the work of Felipe Fernández-Armesto’s 1492: The Year the World Began for a good general overview of the world in the year 1492; and then seek out Silvio Bedini’s The Christopher Columbus Encyclopediaand Samuel Eliot Morison’sAdmiral of the Ocean Sea.
On Medieval Iberia and the Castilian and Portuguese monarchies, begin with Henry Kamen’s comprehensive Spain’s Road to Empire: The Making of a World Power, 1492–1763, and Nancy Rubin’s highly readable Isabella of Castile: The First RenaissanceQueen.
On the papacy of Alexander VI, begin with Christopher Hibbert’s entertaining and shocking The Borgias and Their Enemies, 1431–1519. For a broader look at the history of the popes in general, read Eamon Duffy’s Saints and Sinners: A History of the Popes.
Like other famous explorers, Ferdinand Magellan has shelves of books devoted to him. I would recommend Tim Joyner’s Magellan for a concise background and Laurence Bergreen’s Over the Edge of the World: Magellan’s Terrifying Circumnavigation of the Globe for a rollicking popular account.
A good background in the history of global trade can be found in William J. Bernstein’s A Splendid Exchange: How Trade Shaped the World.
For additional information on Hernán Cortés and the Spanish conquest of the Americas begin with Buddy’s Levy’s Conquistador: Hernán Cortés, King Montezuma, and the Last Stand of the Aztecs.
Piracy in the Caribbean is a wide-ranging and popular topic that ranges over a century and a half. Harry Kelsey’s Sir Francis Drake: The Queen’s Pirate is a solid, readable account of the early days of the sixteenth century, when the struggle over the Treaty of Tordesillas was still at the forefront.
The topics of colonialism and colonial expansion by European powers likewise have had literally hundreds of books devoted to them. There are many excellent ones, but I found Jonathan Hart’s Empires and Colonies to be a good detailed overview. On Portuguese maritime expansion, look to Malyn Newitt’s A History of Portuguese Overseas Expansion, 1400 –1668 and A.R. Disney’s A History of Portugal and the Portuguese Empire.
A readable and interesting look at the history of cartography is John Noble Wilford’s The Mapmakers.
On the history of Hugo Grotius and the origins of international law, there is unfortunately little published for a general audience. Martine Julia van Ittersum’s Profit and Principle: Hugo Grotius, Natural Rights Theories and the Rise of Dutch Power in the EastIndies, 1595–1615 is certainly comprehensive and detailed, but will require a significant effort to read for those very reasons.