Canada has a long history of paper money. The first recorded use of paper as a means of money, was June of 1685 in "New France". Desperate for money to pay the troops, and supply ships nowhere to be seen, the Governor took a deck of "Playing Cards" and wrote "pledges" on the back. Since most of the people in the colony at the time could not read, the cards where then cut into quarters to indicate the denomination. This practice continued on until the late 1710's.
Card board was used again from about 1730 (card money), to sometime in the 1760's. Army scripts and Treasury notes where also used.
The Provincial Governments issued their own currencies (since "Confederation" hadn't occurred yet, the Provincial Governments were effectively countries).
The Province of Canada was formed in 1841 with "Upper Canada" (Ontario) and "Lower Canada" (Quebec). This was not a very successful union and was finally replaced with Confederation in 1867.
From early on, Banks and other Financial Institutions issued their own notes. Their "chartered" was issued by the various Governments of the day. Well over 100 of these "Chartered" banks have come and gone, with only a handful left.
By 1870, with Civil War in the US, and US coins flooding the Canadian market, the new "Dominion of Canada" Government decided it needed to something. New notes were issued, old notes removed from circulation and for the first time, Canadian coins were ordered from the British Mint.
By 1934, the Canadian Government, following the US structure, enacted the "Bank of Canada Act", and in 1935, the first Bank of Canada notes were issued.
All Dominion of Canada and all Bank of Canada notes remain redeemable today at face value.