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The official Enemy Territory manual quotes the role of the medic as follows:

The Medic can heal team-mates with Health Packs and revive dead teammates, bringing them back into combat without having to wait for the next respawn. Medics help their teammates keep on fighting. Medics can only carry the M1A1 Thompson or MP40 SMG's and initially spawn with a load-out of one Hand Grenade.

Medic Special Weapons and Items

• Syringe (Keyboard 5): The Syringe is used to revive teammates (see "Special Abilities" below). When Medics pick up an Ammo Pack, either from a Field Ops or an Ammo Cabinet, they receive 1 extra syringe.
  
• Health Pack (Keyboard 6): Like the Field Ops' Ammo Packs, Health Packs can be dropped on the ground by first switching to them (6) and then pressing Fire. Dropping Health Packs depletes the Power Bar which must be at least half full to drop one. Enemies can also pick up your dropped Health Packs. 

Medic Special Abilities

• Revive: When a teammate dies, Medics will see a red icon over their body. As long as the icon is there, the Medic can revive them by using the syringe (5). Stand over a teammate to bring up the gray Syringe icon, then press Fire to revive. The icon disappears when the team-mate goes into Limbo. This happens when either the body takes too much damage or when the teammate selects to enter Limbo.

This is pretty theoretic and only explains why the medic class was created for. Now when you play on servers, you will very often see medics running around with their weapon and going for kills instead of following team mates with needles to revive. It surely shows that people have not realised yet how important medic ability is. Will they ever? (See post on Rambo medics)  The ability revive gives to not have to respawn is very often the key to victory. When you play as a medic, you have to keep in mind that your team mates' lives are more important than yours. Few people succeed to think like that and that's why there are not many good medics in Wolfenstein ET. The ideal way to team play as medic is:

1. Heal
2. Revive
3. Provide covering fire

Medic is the hardest class and should be the last class for you to play with when discovering ET. It requests you to be patient, often to sacrifice to revived team mates, waiting for them at spawn to regroup. Also you have to know maps well so you do not need too much time to find mates waiting for revives on objective paths. You can't be a good medic without moving fast, jumping, proning, hiding behind mates when needed, sneaking, being able to change weapons fast and use needle correctly.

In case you play this game to win maps (objective), your objective will be your team and not to kill the other team. Indeed once you are able to do all that you can also go for kills but this level of gaming needs time. ;)

Some tips:

• You can pull mates waiting for revives when they are on the ground to hide them in a corner or behind a wall (not in etpro or etmain)
• You can push revived team mates, who still have invulnerability and can't move, to gain time.
• You can hide behind revived team mates who are invulnerable when an enemy is firing at you.
• You can kill/revive a mate when he has low hp to gain time and energy. (Instead of throwing med packs)