There are no character "classes" in Shadowrun, players can choose to mix and match skills and abilities within the rules to create their own unique blend of character. There are some general archetypes that characters do tend to fall into. Beyond these however is a broad range, from small business owners to scientists, entertainers, investigators, any sort of character can be created.
Skilled at computer programming and maneuvering through the virtual reality grid of the Matirx. Deckers use custom built computers knows as cyberdecks in conjunction with datajacks that allow them to project their minds directly into the Matrix's complex reality. By (usually illegally) logging on to the Matrix, deckers can run search routines, tap phone calls and break into system to retrieve data. They use a variety of programs to help them in their tasks including attack and defense programs to engage in cybercombat with other deckers or Intrusion Countermeasure (IC) security programs.
Characters with a piece of Cyberware known as a vehicle control rig (VCR) installed in their body. The VCR allows them to interface directly with suitably adapted vehicles, seeing through the vehicle's sensors and controlling it as if it were their own body. A VCR is required for rigging. Riggers might specialize in drones, vehicles or even be security riggers who jack into buildings security systems to become living monitors.
Physically enhanced combat monsters, Street Samurai rely heavily on Cyberware implants as they attempt to be the quickest, meanest and strongest killing machines. Some fight for honor, some just to get paid.
Mages are one type of magician character, known for using magic in a scientific manner. To mages, magic is about knowlege and structure. Mages cast spells, perceive and project astrally, and conjure elemental spirits.
Magicians who follow a totem spirit. Usually the totem is an animal such as a Coyote or Bear that embody the totems characteristics. For Shamans, magic is attunement with forces of nature. Like Mages they can perceive and project into the astral realm however they conjure nature spirits or Spirits of Man.
Characters who use magic to enhance their natural abilities, their magic tends to be focused inwards rather then outwards. Often adepts use their magic to enhance their body's abilities in combat though some have adept abilities that manifest in quieter ways like artistic abilities.