The public transportation network in Brussels (and in Belgium in general) is really extended and you’ll will easily be able to go from one place to the other using the metro, tram, train or bus, at least during day time (from around 6AM to 11PM).

The companies that manage the public transportation system are:

- STIB/MIVB for metro, trams and buses within the Brussels city limits, plus the bus to Brussels Airport

- TEC and DE LIJN for buses to Wallonia and Flanders respectively

- SNCB/NMBS (Belgian Railways) for trains

The metro network is really easy to figure out. It's essentially 2 lines (one going around the boulevards that are the limits of the city of Brussels itself (the Pentagon) and one crossing the city from east to west with 2 branches at each extremities.
Line 1A starts at Belgium's biggest stadium: King Baudouin and stops at : Heysel (for the Atomium, Bruparck, King Baudouin stadium and Heysel exhibition grounds). It joins line 1B at Beekant and among useful stops: Ste-Catherine, de Brouckere (for rue Neuve, Place de Brouckere and Grand'Place), Gare Centrale (Central station), Parc (for the Royal Park), Arts/Loi for the ministeries and embassies, Schuman for the European District. It splits again from 1B at Merode. The Line 1B starts at Erasme hospital, one of Brussels's biggest universty hospital, it then joins 1A to cross the city centre and splits at Merode, Alma is the stop you want for the faculty of medicine campus of the University of Louvain-La-Neuve and the St-Luc University hospital. The end of the line is at Stockel.
Line 2 almost completely circles the city. Important stops are Rogier (for rue Neuve and hotels around Place Rogier), you can catch the tram there), Botanique (for the Botanical Garden), Arts/Loi (where Line 1 crosses Line 2), Porte de Namur (to access Matonge, the African neighborhood and chaussee d'Ixelles shopping), Louise (for luxury shopping on Avenue Louise and hotels), Porte de Hal (for those nightowls who want to go to the Fuse or eat at Le Bazaar or the early birds who feel like walking to Place du Jeu-de-balles for the flea market) and Gare du Midi (Midi Station), where you can catch Thalys and Eurostar trains.

Website: the metro map is here http://www.stib.irisnet.be/FR/31000F.htm 

Crossing the middle of the city is an underground portion of the tram lines (also called "pré-métro"), very useful and busy. The important stops: Gare du Nord (North Station), Rogier (for rue Neuve), de Brouckere (where you can catch the metro), Bourse (for the stock exchange and Grand'Place) and Gare du midi (Midi station).
But the above ground tram is really a great way to explore the city as it has its own space on the road and is little affected by traffic. Among the interesting lines: Line 92 starting in the North at the Schaerbeek railway station, crossing the Upper-Town (stops at the Museums of Fine Arts, Royal Square, Petit Sablon, Palace of Justice, Avenue Louise (you can catch the Line 2 metro), Place Stephanie and crossing St-Gilles before reaching the affluent borough of Uccle and the end of the line at Fort-Jaco, close to the Foret de Soignes (Soignes Forest) where many Bruxellois spend their Sundays.
Line 93 has the same itinerary as Line 92 except it splits at Place Stephanie to go towards the Universite Libre de Bruxelles (ULB), Brussels's biggest university. Line 81 is a nice alternative to go to the Heysel if you don't want to spend your time underground. It is longer - starts at Montgomery and goes from there via Ixelles to Gare du Midi, then underground to Gare du Nord before heading up to Heysel. Line 44 is also important: you can catch it inside the Montgomery metro station (Line 1B) and it will take you through some fancy neighbourhoods through the Forêt de Soignes all the way to suburban Tervueren and the Museum of Central Africa.

The third transport option is the bus.
There are a lot of lines so this describes one of them: line 71. A very famous "double-bus" line that crosses the most important area in the center of Brussels before reaching Ixelles and the University campuses.
Line 71 starts at Place de Brouckere and stops by the Galeries St-Hubert, Central station, Place Royale (for the museums of Fine Arts and the Music Instruments museums), Parc Royal and Royal Palace, and Porte de Namur (you can reach Avenue Louise with a short walk) before taking the Chaussee d'Ixelles (some good shopping to do there or you can visit Matonge, the Congolese neighborhood) as it gets deeper into Ixelles, you'll pass by l'Amour Fou (a very popular bar), La Maison de la Radio (Radio House) on Place Flagey, a recently renovated building that looks like an ocean liner and used to house the first years of the belgian National radio. It is now a cultural center where you can see concerts and the bar has become quite popular. Just after is the stop of les Etangs d'Ixelles (Ixelles Ponds), 2 ponds that are a little oasis (many students come here to relax, you'll also see families on Sundays and elderly ladies feeding the ducks). The tram carries on to the main University campus (or Campus Solbosch) then, to the Campus shared by the ULB and VUB (its Flemish counterpart) or Campus de La Plaine and finishing its run at Delta where you can catch the metro.
Line 71 is now famous because it is the first line in Brussels that has a night service: the N71. It only works on Friday night s though and until 3:00 am but for a city that never had night services, it's a start.

Website: Network map is here http://www.stib.irisnet.be/FR/34000F.htm

Nightbus map is here: http://www.stib.irisnet.be/FR/33000F.htm 

Information and map

At any metro or train station, you can get a complete map of the network and buy STIB/MIVB cards. You can also some of the STIB/MIVB cards in trams and buses. There are also commercial bureaux where you can buy all sorts of cards:

- Bureau ”Toison d’Or” (avenue de la Toison d’Or, 14, 1050 Brussels) : open Mon.-Sat. 10AM to 6PM
- Metro Station ”Porte de Namur” : open Mon.-Sat. 8AM to 5.30PM
- Metro Station ”Rogier” : open Mon.-Fri. 10AM to 5.30PM, Sat. 8AM to 5PM
- Metro Station ”Gare du Midi” : open Mon.-Fri. 7.30AM to 5.30PM, first and last Sunday of the month 8.30AM to 2PM
- Bureau ”De Brouckère” (rue de l'Evêque, 2, 1000 Brussels) : open Mon.-Sat. 10AM to 6PM
- Metro Station ”Roodebeek” : open Mon.-Fri. 10AM to 5PM, first and last Saturday of the month 10AM to 5PM

BOOTIKs at various metro stations, e.g. Mérode, Montgomery. 

Cards and fares

These cards allow you to travel on the metro, bus, tram and train systems (except on lines 11/12 between NATO and Brussels Airport and on the special night buses that run between midnight and 3 a.m. on Friday and Saturday nights):

- 1-trip card: €1.50 if bought before boarding the means of transport; € 2.00 if bought from the bus or tram driver

- 5-trip card: € 6.70 (not nominative)
- 10-trip card: € 11 (not nominative)
- 1-day card: €4 (valid for unlimited travel for one day for one person; on Saturdays, Sundays and public holidays, this card is valid for 2 people)
- 3-day card: €9.00 (valid for unlimited travel for 3 days for one person)

 - Brussels Card: €20, €28 or €33 for 24h, 48h or 72h respectively, valid for unlimited travel on the STIB network during this period (except the airport bus between NATO and the airport and night buses), gives free access to most of the museums and discounts to other attractions; you can also buy this card at most hotels, tourist offices and museums.

Note: At the entrance to metro/pre-metro or (within Brussels city limits) train stations, and after boarding an overground tram or bus, you have to punch your card in one of the orange machines. For day and multi-day cards, this starts the period for which they are valid, for single-trip or multi-trip cards this marks the time from which you can travel on the STIB/MIVB network during one hour: however, single and multi-trip cards must also be inserted into the machine in each new means of transport taken during the 60 minutes, in order to mark the transit. If you do not and there is a control, you will get fined (controls are very frequent).

Please also note that it is now obligatory to board most buses (except the long "bendy-buses", before 20.00 hrs) only at the front so that the driver can check that passengers punch their tickets or show a pass. 

Art in the metro

Many metro stations are worth a stop as they have been beautifully decorated by famous Belgian artists. Metro station “Anneessens” is decorated with paintings by Alechinsky and Dotremont, “Bourse/Beurs” with paintings by Paul Delvaux, “Montgomery” with painting by Folon, “Stockel” with comics of Tintin, Horta with cast-iron by Horta, “Porte de Hal” with paintings by Schuiten.

Website : http://www.stib.irisnet.be

For more info, call (+32) 2 512 2000 or from within Belgium, 02/512 2000