Metro This is probably all you will use, if sticking to the city centre, which is compact and walkable. Much of the metro is old-fashioned, in complete contrast to the gleaming new additions. The work is ongoing, and much needed. Line 1 (green) runs from the port at Piraeus to the northern suburb of Kifissia. Line 2 (red) runs from Syntagma Square to the western suburb of Daphni. Line 3 (blue) runs northeast from Syntagma Square and will ultimately reach the airport. At present the terminus is at Ethniki Amyna, with a shuttle bus to the airport.

There are two types of ticket. The cheaper is valid across two zones but on Line 1 only, and the slightly more expensive allows one-way travel across all 3 zones for up to 90 minutes. The simplest thing is to ask at the ticket window.

Bus One look at a typical packed Athens bus and you will know why few tourists bother with them. However, they are the cheapest way of getting around, and the network covers the whole city. Buy your ticket in advance from the kiosk near every stop, and frank it in the machine when you board the bus. One ticket is valid for any one journey, provided you do not change buses.

Taxi The yellow taxis are cheap and can be hailed in the street, booked from your hotel, or you can go to the main ranks on Syntagma Square and in front of the National Gardens. Greek taxis are also shared, and can pick up other passengers going in the same direction. This is why you will see local people waving at taxis with passengers in them and shouting out their own destination. All passengers pay the metered fare, it is not shared between them.

Some drivers are rogues and see tourists as fair game. Check that the meter is on. Make sure you have some idea of what the fare should be, and stick to it. In disputes, ask your hotel for help, insist on contacting the Tourist Police or find the nearest regular policeman. If the taxi driver is cheating you, he will probably back down for fear of losing his license. But do remember that there are also legitimate surcharges for journeys to the airport, to train and ferry terminals, after midnight and for every piece of luggage carried.

Top Tip: The bus ticket from the airport is also a one-day travel card, which can be used throughout the Athens public transport systems. This is useful to know if you arrive early enough in the day.

Acropolis (Tel: 010 321 0219. Open daily Apr-Oct 8am-7pm, Nov-Mar 8am-sunset). Unmissable: literally so as you can see the Parthenon building from throughout the city. It was on and around this rock that the city was founded, and the collection of buildings that crown it mostly date from about the 5th century BC: the Golden Age.

Agora (Adrianou 24, Tel 010 321 0185. Open Tue-Sun 8.30am-3pm). The market place of ancient Athens covers a large area and is second only to the Acropolis as a must see site. It was in use as a market place as long ago as the 6th century BC, and some of its history is told in the site museum. This is housed in the Stoa of Attalos, an elegant arcaded building from the 2nd century BC which has been immaculately restored. The Agora site also contains a church and the beautiful Temple of Hephaistos, amongst other treasures.

First Cemetery of Athens On Anapafsios is the cemetery where Athens most prominent citizens are buried. Here can be found the graves of the archaeologist Heinrich Schliemann, who discovered Mycenae, and the famous Greek politician and actress Melina Mercouri.

Hadrians Arch This was built in the 2nd century AD by the Emperor Hadrian, and marks the boundary of the old city. On one side an inscription tells people that they are in the ancient city of Athens, while on the other side the inscription informs you that you are in the modern Roman city.

Keramikos Cemetery At the far end of Ermou is what was the principal cemetery of ancient Athens. This was the potters quarter of the city, hence the name. There are tombs here dating back to the 12th century BC, and also a small museum on the site. (Open Tue-Sun 8.30am-2.30pm).

Mitropolis The citys Greek Orthodox Cathedral is a modern building, and grander on the outside than on the inside. Dont miss the tiny 12th century church next to it, the Little Mitropolis, which is like stepping into a cool cave.

Odeon of Herodes Atticus This grand theatre stands below the southern slopes of the Acropolis. It was built in AD161-174 by the Roman Consul after whom it is named, and seats 5000 people. It has been restored and is used today for the annual summer Athens Festival.

Olympic Stadium (Leoforos Ardhittou. Open daily sunrise-sunset). This perfectly designed little stadium was built in 1896, when the Olympic Games were revived in their country of origin. It is on the site of an earlier stadium, where contests were held from the 4th century BC onwards. Today you can admire its sweeping curves, or watch modern Athenians jogging around the track. Photographers will have a field day, especially with the repeated patterns of the rows of seats, which can hold up to 60,000 people. It is used as the finishing point for the Athens Marathon, held every October.

Pnyx South of the Acropolis and across the road is the hilly retreat known as the Pnyx. Fewer visitors come here, except in the evenings for the Sound and Light Show. The seating for this is in the place where the Assembly of ancient Athens would meet to debate, in the 18,000-seat amphitheatre.

Presidential Palace This was the Royal Palace, until the Greek Monarchy was abolished in 1974. It was built in 1878, and restored in 1935 when it also became the home of the Greek Parliament. The building can be found, closely guarded, on Irodou Attikou, behind the modern Parliament Building.

Temple of Olympian Zeus Though now mostly in ruins this was once the largest temple in Greece. The size of the remaining 15 columns does give you an impression of its scale. It was begun in the 6th century BC but not completed until AD 132, by the Emperor Hadrian.

Theatre of Dionysos On the southern slopes of the Acropolis are the remnants of this theatre, which could once hold 17,000 people. The present remains were built in 342-326BC, though a wooden theatre was here before that. The site has seen everything from gladiatorial contests to the birth of modern European drama, with works by Sophocles, Aristophanes and others being performed here. Open daily in summer 8am-7pm, in winter 8am-2.45pm.

Tower of the Winds Inside the Roman Agora but easily seen from outside too. The beautiful octagon building dates from about 40BC. Each side has a frieze depicting the eight wind gods. It also has a weather vane, compass and sundials, but no longer the water clock which was powered by a stream from the Acropolis.

Top Tip: Dont visit the Keramikos Cemetery on Sunday morning. The Monastiraki flea market is packed then, and it can take a long time to make your way through the dense crowds.