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Returning to the cathedral and the pleasant square that it shares with the Archbishop's palace, one is aware of the fortress wall of the Alcazar opposite. Inside is the delectable 14th-century palace that was mainly built by Pedro the Cruel, but there have been many additions. The heart of the palace is the large courtyard, where all the decoration seems to be Islamic until one finds the miniature heads and the coats-of-arms amid pine kernels and leafy interlace. The most gorgeous hall is the Salon de Embajadores, or Ambassadors, with an astonishing intermeshed dome and reflected light that subdues the dazzle of the tile dadoes and multiplicity of ornament. The Mudejar craftsmen came from Toledo and Granada, where the Sultan was a friend of Pedro. The lavish gardens, palm and orange groves center on a tiny 16th-century pavilion built for Charles V, and they are frequented by cats that befriend the lonely. Deeper in the old city, the Duke of Medinaceli's palace is supposed to be inspired by the non-existent House of Pontius Pilate in Jerusalem. Its courtyard is full of ugly Roman provincial statuary, but the smaller garden court's charm and the upper terrace approached by a splendid staircase is magnificent - a spacious retreat. If ever the Mudejar style went too far it is here that it happened; the building tries to say too much with all the restlessness of too much ornament. But Mudejar lived to fertilize Art Nouveau and even the enormous Plaza de Espana, center of the 1929 World's Fair and now municipal offices. It is more baroque than anything else, certainly in scale, but do not overlook the panels of ceramics depicting great events in Spanish history, such as the surrender of Granada to [Ferdinand III] and Isabella. These transform the mud and dross of medieval times into an immaculate world that never was. Go on a weekend when the forecourt is thronged with families and lovers, the boats are out on the canals and basins and the empty offices are forgotten in a carnival of balloons and cotton candy. The Duke of Medinaceli's palace is open from 10 A.M. to 1:30 P.M. and 4 P.M. to 7 P.M. Admission is $1.65. The cathedral is open weekdays 11 A.M. to 6 P.M.