Budapest Metro
The public transport system in Budapest is excellent. The Budapest Metro has 4 lines, one of which is currently under construction namely Metro Line 4. The 3 main lines all meet at Budapest city centre at the Deak Ferenc Ter station.
The Budapest Metro runs between 04.30 and 23.10 daily, with trains every 4-5 minutes albeit every 2 to three minutes during rush hour. After 8.00pm the trains return to fixed timetable although still run every 10-15 minutes on average. You can obtain a good map of the Budapest metro network at any of the major stations.
Tickets must be bought in advance which is sometimes frustrating for Budapest tourists as they are not always sure of where to buy tickets. Tickets cost 270 HUF however I would suggest either buying a 1-3 day pass or purchasing a ticket booklet with multiple tickets. The prices of the passes are as follows 1-Day-Pass - 1550F / 3-Day-Pass - 3400F / 7-Day-Pass - 4000F. Alternatively if you purchase a Budapest Card you get free public transport included in the price.
Budapest has an open fare system, there is no barriers to the metro, buses or trams. Some of the Budapest metro stations have ticket machines with touch screen in 4 main languages namely English, Hungarian, German, and Italian). There are ticket police who patrol the trams, metros, stations and otherwise so I suggest you buy a ticket or face a fine.

In Budapest there is a three line system, with all lines meeting in the city centre at Deák Ferenc Tér.
M1 5 km in length was first opened in 1896 between Vörösmarty tér in the centre and Széchenyi fürdõ as the first electric underground (Földalatti) line in Europe. About 80 years later this line was further extended to Mexikói út. This line is different from the other two metro lines in size. It runs directly under the street and is only 6 metres wide and 2.75 metres in height.
M1 Line Underground.

Vörösmarty tér - Deák Ferenc tér - Bajcsy-Zsilinszky út - Opera - Oktogon - Vörösmarty utca - Kodály körönd - Bajza utca - Hősök tere - Állatkert - Széchenyi fürdő - Mexikói út
M2 10 km in length is an east-west line connecting both the major railway stations, Déli (South station) and Keleti (East station), surface between Pillangö utca and the eastern terminus Örs vezér tere. Although construction had started already in the 50's, this line was only opened between 1970 (Deák Ferenc tér - Örs vezér tere) and 1972 (Deák Ferenc tér - Déli pu.). In autumn 2003, M2 started to undergo total refurbishing. This is the most used line in the Budapest Metro network.
M2 Line East-West line
Örs vezér tere - Pillangó utca - Stadionok - Keleti pályaudvar - Blaha Lujza tér - Astoria - Deák Ferenc tér - Kossuth Lajos tér - Batthyány tér - Moszkva tér - Déli pályaudvar

M3 18 km in length is a north-south connection on the Pest side of Budapest. Apart from the southern terminus Köbánya-Kispest, all stations are underground. The first part (Deák tér - Nagyvárad tér) opened in 1976, in various stages it has been extended in both directions.
M3 Line North-South Line
Kőbánya-Kispest - Határ út -Pöttyös utca - Ecseri út - Népliget - Nagyvárad tér - Klinikák - Ferenc körút - Kálvin tér - Ferenciek tere (formerly: Felszabadulás tér) - Deák Ferenc tér -Arany János utca - Nyugati pályaudvar - Lehel tér (formerly: Élmunkás tér) - Dózsa György út - Árpád híd - Forgách utca - Gyöngyösi utca - Újpest-Városkapu - Újpest-Központ - There is a planned extension towards Káposztásmegyer in the northeast and Ferihegy Budapest airport possibly by 2010.