El Al Israel Airlines. There are also two much smaller carriers, called Arkia and Israir.
In total, there are nine (9) airlines located in Isreal. These airlines are: Arkia Isreal Airlines, Ayit Aviation and Tourism, CAL Cargo Air Lines, Chim-Nir Aviation, El Al, Elrom Airlines, Israir Airlines, Orange Aviation, Tamir Airways.
Ben Gurion Airport is the hub of El Al, Israir Airlines, Arkia Israel Airlines and Sun d'Or International Airlines. Any of these are good options. See the related link for the airport's website for other airlines and contact information.
Amsterdam Airlines was created in 2007.
L'Express Airlines was created in 1989.
SkyBahamas Airlines was created in 2006.
VLM Airlines was created in 1993.
MCA Airlines was created in 2008.
Ransome Airlines was created in 1967.
Cronus Airlines was created in 1994.
Atlantis Airlines was created in 2001.
Aeromech Airlines was created in 1951.