The Renaissance, which flourished in Italy- big surprise- before eventually making its way through the rest of Europe, was essentially a classical revival. Using clean forms and little decoration, elements like columns, simple shapes, and symmetry made a big come-back.
Early Renaissance in Granada
However, Spain has always had a certain affinity for decoration and didn't quite hop on the Renaissance train as easily as other countires. The earliest part of the Spanish Renaissance- especially in southern Spain- gave rise to a style known as "Plateresque" which was essentially everything that the genuine Italian Renaissance was not. Incorporating Gothic and Moorish architectural and decorative elements, the Plateresque period was extremely stylized and shows up most frequently adorning building façades. Little attention was paid during the Renaissance Plateresque period to structure- the bulk of the focus was on taking surface decoration to new heights.
In Granada there are several examples of Plateresque. The most imposing is undoubtedly the cathedral- just take a look at its giant domed rotunda and you'll see what we're talking about!
Late Renaissance in Granada
During the 16th century, Spain began to really catch on to the "High Renaissance" style. Different in every way from the preceding Plateresque Renaissance, the classical forms and decoration that Italy brought back from early Roman and Greek times began to show up in Spain. As the Renaissance neared its end and the subsequent Baroque period, a new style emerged. Headed by Juan de Herrera, who constructed the massive El Escorial outside of Madrid, the style boasts great austerity emphasized by enormous proportions- El Escorial, for example, is the largest building in Spain!
The Palacio de Carlos V, located in La Alhambra, is an illustrative example of this later part of Renaissance architecture. Set in a perfectly square building with exemplary Renaissance façades, within the structure you'll find a large circular patio boasting two floors of arcades of Doric and Ionic columns.