Waterman
Description
Proposer: Marc Waterman, Daan Krammer
Proposed: 1981
Steps:
 Solve the left side layer minus one edge.
 Solve the right side corners.
 Solve three of the right side edges and fine final left side edge.
 Solve the final right side edge and orient the edges of the M layer.
 Permute the M layer.
The Waterman method contains many variants. The one described on this page is known as "Simplified Waterman".
Click here for more step details on the SpeedSolving wiki
Origin
Waterman
The Waterman method was developed in 1981. As booklet was produced describing the method and published as part of Cubing For Fun [1].
Other Similar Methods
Other Watermanlike methods had been published in 1981 or prior.

Johnson, K.C.  The Magic Cube Puzzle  1979
 First layer
 Solve last layer corners
 Solve the last eight edges.

Truran, Trevor  Solving That Eastern Bloc(k)  1979
 First layer
 Permute last layer corners
 Orient last layer corners
 Solve the last eight edges.

Cairns, Colin & Dave Griffiths  Teach Yourself CubeBashing  1979
 An extended version of Truran's publication

Angevine, James  Solution for the Magic Cube Puzzle  1979
 The same as Carins and Griffiths, which is the same as Truran

Ollerenshaw, Dame Kathleen  The Hungarian Magic Cube  1980
 First layer
 Last layer corners
 Middle layer edges
 Last layer edges.

Bossert, Patrick  You Can Do The Cube  1981
 First layer corners
 First layer edges
 Bottom layer corners
 Remaining edges.
Much of this information is found in David Singmaster's Notes on Rubik's 'Magic Cube'. I reached out to Georges Helm, who owns copies of these books. He kindly wrote out the steps of the methods in each book. Waterman and Kraamer's development of the Waterman method is likely the most thorough of them all with hundreds of edge solving algorithms developed, full CLL, and a recognition method for CLL.
References
[1] M. Waterman and A. Treep, "Waterman Method," Cubsim For Fun, 1987. [Online]. Available: https://web.archive.org/web/20071029152943/http://rubikscube.info/waterman/booklet.php.