The purpose of this paper is to research the air waybill and the carrier's liability in respect of the carriage of cargo by air under the Montreal Convention of 1999. The Warsaw Convention for the unification of certain rules for international carriage by air was adopted in 1929 and modified successively in 1955, 1961, 1971, 1975 and 1999. The Montreal Convention of 1999 modernized and consolidated the Warsaw Convention and related instruments. Under the Montreal Convention, in respect of the carriage of cargo, the air waybill shall be made out by the consignor. If, at the request of the consignor, the carrier makes it out, the carrier shall be deemed to have done so on behalf of the consignor. The air waybill shall be made out in three orignal parts. Under the Montreal Convention, the consignor shall indemnify the carrier against all damages suffered by the carrier or any other person to whom the carrier is liable, by reason of the irregularity, incorrectness or incompleteness of the particulars and statement furnished by the consignor or on its behalf. The air waybill is not a document of title or negotiable instrument. Under the Montreal Convention, the air waybill is prima facie evidence of the conclusion of the contract, of the acceptance of the cargo and of the conditions of carriage. If the carrier carries out the instructions of the consignor for the disposition of the cargo without requiring the production of the part of the air waybill, the carrier will be liable, for any damage which may be accused thereby to any person who is lawfully in possession of the part of the air waybill. Under the Montreal Convention, the carrier is liable by application of principle of strict liability for the damage sustained during the carriage of cargo by air. The carrier is liable for the destruction or loss of, or damage to cargo and delay during the carriage by air. The period of the carriage by air does not extend to any carriage by land, by sea or by inland waterway performed outside an airport. Under the Montreal Convention, the carrier's liability is limited to a sum of 17 Special Drawing Rights per kilogramme. Any provision tending to relieve the carrier of liability or to fix a lower limit than that which is laid down in this Convention shall be and void. Under the Montreal Convention, if the carrier proves that the damage was caused by the negligence or other wrongful act or omission of the person claiming compensation, or the person from whom he derives his rights, the carrier shall be wholly or partly exonerated from ist liability to the claimant to the extent that such negligence or wrongful act or omission caused the damage. Under the Montreal Convention, any action for damages, however founded, whether under this Convention or in contract or in tort or otherwise, can only be brought subject to the conditions and such limits of liability as are set out in this Convention. Under the Montreal Convention, in the case of damage the person entitled to delivery must complain to the carrier forthwith after the discovery of the damage, and at the latest, within fourteen days from the date of receipt of cargo. In the case of delay, the complaint must be made at the latest within twenty-one days from the date on which the cargo has been placed at his disposal. if no complaint is made within the times aforesaid, no action shall lie against the carrier, save in the case of fraud on its part. Under the Montreal Convention, the right to damage shall be extinguished if an action is not brought within a period of two years, reckoned from the date of arrival at the destination, or from the date on which the aircraft ought to have arrived, or from the date on which the carriage stopped. In conclusion, the Montreal Convention has main outstanding issues with respect to the carrier's liability in respect of the carriage of cargo by air as follows : The amounts of limits of the carrier's liability, the duration of the carrier's liability, and the aviation liability insurance. Therefore, the conditions and limits of the carrier's liability under the Montreal Convention should be readjusted and regulated in detail.