Air Algérie (https://airalgerie.dz) offers extensive and reasonably priced domestic services, including flights to Tamanrasset and Ghardaïa. Its safety record is generally pretty good and flights are fairly punctual.
Tassili Airlines (www.tassiliairlines.aero) has an extensive domestic network linking most big northern cities with each other and Algiers with southern desert cities. For long-distance north–south travel, going by plane is by far the most comfortable, and safest, way to travel.
Travelling around Algeria is perfectly feasible, but roads linking northern cities can be busy and scary and distances very long in the south. Avoid cycling in the Sahara in the summer. It's possible that the authorities might forbid you from cycling in the Saharan regions at any time of year.
There are no navigable rivers in Algeria.
Long-distance buses are run by various regional companies and are usually reasonably comfortable. Routes go as far south as Tamanrasset. Try to buy your ticket at least a day ahead: less frequently serviced Saharan routes sell out. Bus service in the north is extensive and reaches most towns. Getting to archaeological sites by bus, however, can sometimes be difficult.
Car & Motorcycle
Driving yourself anywhere in the country theoretically requires an agency escort, but it's not strictly enforced in the north, even with numerous police checks. The Kabylie region in Algeria's northwest can be dangerous for unescorted nonresidents and you should never drive here after dark.
The main route across the Sahara is the Route du Hoggar, from Ghardaïa via El-Goléa and In Salah to Tamanrasset and on to the border and Arlit in Niger. The road is tar all the way to In Guezzam. Other less-used roads include the eastern Route du Tassili N'Ajjer, from Hassi Messaoud to Tamanrasset across the Grand Erg Oriental, and the Route du Tanezrouft, from Adrar to Borj Mokhtar near the Malian border. The latter two routes include sections of sandy track known as piste. For all these southern routes a tour agency escort is obligatory. Do not attempt any pistes without a sturdy 4WD.
In the north fuel stations are common. In the south fill up in all major towns as you won't find anything out in the desert. Fuel is very cheap (diesel is around DA14 per litre and petrol DH25 to DH30 per litre.
Note that Algerian drivers can often be reckless in the extreme and with generally good roads they can – and do – go very fast. Accidents are very common and over 3700 people died on Algerian roads in 2016. Expect lots of near misses.
Louages (share taxis) only operate in the north of the country. They are often more expensive than buses, but they're faster although that's not always a good thing!
SNTF (Société Nationale des Transports Ferroviaires; www.sntf.dz) trains run from Algiers along the eastern line to Bejaia, Constantine and Annaba (seven to 10 hours) and along the western line to Oran (four to six hours) and from there to Tlemcen (2½ hours). Additional lines run south from Oran to Béchar and from Constantine to Touggourt.
The trains are fairly modern and are generally punctual and at least as fast as road travel.