Córdoba's 10 most significant monuments span 2,000 years of continuous history: the Mezquita-Catedral (856 columns, begun 784 by Abd al-Rahman I, €20 entry), the Roman Bridge open free at any hour, and the ruined caliphal palace of Medina Azahara 8km west of the city. All are within 1km of each other in the UNESCO World Heritage zone.
The Islamic layer is the one that shocks visitors most. The Mezquita's 856 columns are just the part you can see from the nave. The full building once covered an area larger than St Peter's Basilica in Rome. Outside the walls, the caliphal city of Medina Azahara was built in less than a generation and destroyed in less than one, its marble slabs stripped and scattered before the 11th century ended. The ambition of what Abd al-Rahman III attempted there (a new capital to rival Baghdad and Constantinople) only becomes clear when you stand in the Salon Rico and count the fragments they've managed to reassemble.
This list runs in order of significance for a first visit, then shades toward the less obvious. The top five are genuinely unmissable. From the sixth entry onward, you're in the territory most visitors skip, and where some of the best hours in Córdoba are spent. Three days is the comfortable minimum. Plan the Mezquita for early morning before the groups arrive, Medina Azahara for a weekday, and leave at least one afternoon for the quieter sights in the Judería.