Nautilus

Nautilus is a speedsolving method developed by James Straughan. It was originally developed in 2006 but was redeveloped with additional variants starting in 2020.
Contents
Steps
The first step is to solve the first two layers minus a square. Typically this would be the dFr square (DF edge + DFR corner + FR edge). However the dBr, dfR, or dbR squares can also be left empty. There are a few good approaches to building this shape. If the empty square is at dFr, the standard way is to build a 1x2x3 at dL then a 2x2x2 at dbr. Users can also build a 2x2x2 at dbl, the pair at DFL+FL, and the square at dbR. Another good option is to solve the first layer minus the DF edge and DFR corner then add the three ESlice edges.
Before, during, or after the primary shape, all edges can be oriented to reduce the number of cases for proceeding algorithmbased steps. After the first step, the solve is completed using one of several variants.
Variants
LL
 Completely solve the empty square. This can be performed intuitively or with algorithms. If all edges are oriented, it is 117 algorithms that average 8 moves.
 Solve the last layer using any variant.
LSLL
 After the primary method shape, orient all edges while inserting the DF edge.
 Finish using any LSLL method.
CLL + L5E
 Build the primary method shape along with the dFR pair.
 CLL
 L5E. If all edges were oriented, L5EP is used.
2GLL+1
 Build and place the dFR pair while permuting the U layer corners. Orient all edges before this step.
 Solve all remaining pieces. The number of cases for this step is around the same as in ZBLL.
CX
 Solve the remaining five corners. CLL, L5C, or any other method can be used.
 Solve the remaining six edges. If all edges were oriented, L6EP can be used. If not oriented, this step can be split into first solving two or three edges then solving the remaining.
Polar
 Build and insert the dFR pair while separating the left and right side stickers to the left and right side. This means orienting all corners to have their L/R stickers facing L/R and the L/R edges are on the left and right sides.
 Permute all.
CLL+2
 Build the primary method shape along with the dFR pair.
 Solve the U layer corners while also solving any two edges. This step is similar to CLL+1 and would require the use of the same system to develop algorithms.
 Solve the last three edges.
Transformation
 Create any U layer or F layer pair, move it to the UbR position, and perform an R move to place it in the first two layers.
 Move any oriented edge to the UB edge position and perform an M' move to place it in the first two layers.
 Solve the last layer then undo the transformation performed in the previous two steps.
Note: This essentially solves L5C and L5E in fewer moves and cases than if transformation wasn't used. The first step of transforming using a pair or the second step of transforming using an edge are both optional. Just one can be used or both can be used. The images below show transformation applied if the dfr 2x2x2 was solved during the primary method shape instead of dbr.
Pros
 Great lookahead for the rest of the solve after the primary shape is built.
 Most of the solve involves the use of only the dominant hand.
 Good for both two handed and one handed solving.
 Rotationless.
 Low movecount.
Cons
 While r, R, U, M is a great moveset, some algorithms will instead need to be R, U, F for speedsolving.
History
In 2006, the MI1 method was developed. The primary shape in that method was very close to the one in Nautilus. The only difference being that the DR edge wasn't solved. It was found that having the DR edge slot be empty caused problems for ergonomics. So that same year it was decided to solve the DR edge along with the rest of the shape and branch Nautilus off into its own method. This produced much better ergonomics and led to better variants. In 2020 new, more advanced variants were added to the method.