You will only see these contracts upon entering the Animus and joining an alliance.
Spy: Spying on another guard, citizen, Assassin or Templar. These missions typically require you to extract information without killing the person who divulged it, unless stated otherwise.
Battle: These missions may require you to fight others, often Assassins, Templars and Guards. Loss of health and even life is likely. These battle missions may range from small-scale skirmishes into entire wars.
Assassination: Assassination missions are often a favourite of those who undertake them. They require knowledge of the person who is to be killed, their location and a method to perform the assassination with. These must be done as stealthily as possible.
Free: Missions that do not require much thought or action. Examples may be free-running for some coin or practising swordfights. They are a good way to train up your skills or help you earn some more money.
Bodyguard: Sometimes people ask others to guard their lives from those who may want to kill them. Battles are likely and so is loss of life if the person who wants who you are protecting, dead, manages to spring a trap.
Bribe: Save up some Florins for these missions! Sometimes those who you need information from need a little bit of encouraging to loosen their lips...
Interrogation: Sometimes bribery just doesn't work and if this is the case, old fashioned methods may have to be resorted to. When violence doesn't have to be resorted to too much, some torture may be adequate.
Meeting: Meet others, unseen, in select locations. Don't be late or be seen by your foes. Your enemies may be lyng in wait or listening in on the meeting so ensure you aren't overheard.