This set of 12 pDFs was produced somwhat hurriedly in September 2019, when I was expecting to go in hospital for an operation.
The twelve monographs were intended as chapters of a large book, which never found a publisher.
Some errors in the cross-references may be noticed. It is still hoped to produce it in book form in due course.
1 — Theory of Moves
Covers general principles used throughout the study, including Moves, Pieces, Magic and Symmetry
and also covers the Smallest Knight-tourable Boards.
2 — Walker Tours
Covers tours by pieces with lateral and diagonal moves, that is Wazir, Rook, King and Queen.
The Rook and Queen tours being classified according to how many different move-types the piece makes.
3 — Shaped & Holey Boards
Covers knght tours on boards with non-rectangular otlines and possibly with holes.
These are classified according to their degree and type of symmetry. Octonary, Biaxial, Birotary, Aial, Rotary and Unary.
4 — Oblong Boards
Covers knight tours on non-square rectangular boards.
5 — Odd & Oddly Even Boards
Covers knight tours on square boards of sizes 515, 7x7, 9x9, ... and 6x6, 10x10, 14x14, ....
The oddly even boards of side 4n + 2 admit tours with birotary symmetry (unchanged by 90 degree rotation).
6 — Geometry of Chessboard Knight Tours
Cover knight tours on the 8×8 board, with emphasis on angles, and other geometrical features.
7 — Symmetry in Chessboard Knight Tours
Covers knight tours on the 8×8 board including a complete collection of central angle formations.
8 — Octonary & Quaternary Pseudotours
Covers the patterns formed by superimposed circuits, and tours formed from them by 'simple linking'.
9 — Magic Knight Tours
Covers the history of knight tours with magic summation properties, including a complete catalogue.
10 — Augmented Knight & Leaper Tours
Covers tours by pieces that combine the knight with rook and bishop moves,
and also tours by longer leapers like Zebra {2,3}, Giraffe {1,4}, Antelope {3,4} and their augmentations and combinations.
11 — Alternative Worlds
Covers recreations such as Lettered tours, including Cryptotours, Non-crossing paths,
and alternative Board designs, such as Cylinder chess, Space chess, and Honeycombs.
12 — Chronology & Bibliography