Here are some books that help explain the Renaissance context of Shakespeare’s plays.
Jacob Burckhardt, The Civilization of the Renaissance in Italy, trans. S.G.C. Middlemore, 2 vols., illustrated edition (New York: Harper & Row, 1958)—the book that established the concept of the “Renaissance”; still the best book on the subject
Ernst Cassirer, Paul Oskar Kristeller, and John Herman Randall, Jr., eds., The Renaissance Philosophy of Man—edited anthology of translated writings of Renaissance philosophers (Petrarch, Valla, Ficino, Pico, Pomponazzi, and Vives)
Lisa Jardine, Worldly Goods: A New History of the Renaissance (New York: W. W. Norton, 1996)—emphasis on economic developments in the Renaissance
William Kerrigan and Gordon Braden, The Idea of the Renaissance (Baltimore: Johns Hopkins University Press, 1989)—a modern book in the Burckhardt tradition