I have tried to gather references to this book forty years after its first appearance.
This is not so difficult for articles and books that have appeared in the last
decade or two, because of web services like Google Books and Google Scholar.
However, it is more of a challenge for earlier material.
For that reason, I'm somewhat stunned to see an early reference to the book
by a group of such distinguished researchers as
Fan Chung, Paul Erdös, Ron Graham, Stanislaw Ulam, and Frances Yao.
I guess that they recognized just how much was left open by the book!

N. J. A. Sloane,
"The Online Encyclopedia of Integer Sequences,"
OEIS Foundation.

F. R. K. Chung, P. Erdös, R. L. Graham, and S. M. Ulam, F. F. Yao,
"Minimal decompositions of two graphs into pairwise isomorphic subgraphs,"
Congressus Numerantium, issue 23 (1979),
Proc. 10th SE Conf. on Combinatorics, Graph Theory, and Computing, Boca Raton, 1977, pp. 318.
 Jin Akiyama and Gisaku Nakamura,
"Dudeney dissection of polygons,"
Discrete and Computational Geometry: Japanese Conference, JCDCG'98,
Jin Akiyama, Mikio Kano, and Masatsugu Urabe (eds.),
LNCS No. 1763, Tokyo, Japan, December 1998, pp. 1429.
 Jin Akiyama and Gisaku Nakamura,
"Dudeney dissection of polygons,"
Discrete and Computational Geometry, LNCS 1763,
Springer, 2000, pp. 1429.
 Erik D. Demaine, Martin L. Demaine, Jeffrey F. Lindy, and Diane L. Souvaine,
"Hinged dissection of polypolyhedra,"
Algorithms and Data Structures, Lecture Notes in Computer Science Volume 3608,
2005, pp. 205217.
 Timothy G. Abbott, Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine, and Scott Kominers,
"Hinged dissections exist,"
Symposium on Computational Geometry,
2008, pp. 110119.
 Daniel Wyllie Lacerda Rodrigues,
"Detalhes acera da dissecçã do triângulo no quadrado"
V Colóquio de História e Tecnologia no Ensino da Matemática,
Recife, Brasil, de 26 a 30 de julho de 2010.
 Yahan Zhou and Rui Wang,
"An algorithm for creating geometric dissection puzzles,"
Bridges 2012: Mathematics, Music, Art, Architecture, Culture,
pp. 4956.
 Hans Walser,
Puzzle (pdf),
at the SLATagung, in Bern, Switzerland, November 15, 2014.
 Peggy Oglesby,
"Puzzling #129 Nine easy pieces,"
D Magazine, February 1977.
 ??,
"??,"
New York State Mathematics Teachers Journal, Volumes 2729,
1977, p. 132.
 Philip Graham Tilson,
"New dissections of pentagon and pentagram,"
Journal of Recreational Mathematics,
vol. 11 (197879) no. 2, pp. 108111.
 David M. Collison,
"Rational geometric dissections of convex polygons,"
Journal of Recreational Mathematics,
vol. 12, no. 2 (197980), pp. 95103.
 M.S. Klamkin,
"The Olympiad corner: 24,"
Crux Mathematicorum, vol. 7, no. 4, pp. 105115, April 1981.
 C. S. Stuart,
"Some new geometric dissections,"
Journal of Recreational Mathematics,
vol. 15, no. 1 (198283), pp. 1927.
 Peter McMullen and Rolf Schneider,
"Valuations on convex bodies,"
Convexity and its Applications,
Birkhäuser Basel, 1983, pp. 170247.
 ??,
MAA Notes,
issues 15,
Mathematical Association of America,
Committee on the Undergraduate Program in Mathematics, p. 91, 1983.
 Frank Tapson,
"Maths resource,"
Mathematics in School,
vol. 14, no. 1 (January 1985), pp. 1823.
 Barbara Rabijewska and Mieczyslaw Trad,
"A mathematical camp for bright pupils,"
Educational Studies in Mathematics,
vol. 16, no. 1 (February 1985), pp. 4157.
 C. S. Elliott,
"Some more geometric dissections,"
Journal of Recreational Mathematics,
vol. 18, no. 1 (198586), pp. 916.
 Medhat Hishmat Rahim,
"Laboratory investigations in geometry: a piecewise congruence approach,"
International Journal of Mathematical Education in Science and Technology,
vol. 17, no. 4 (1986), pp. 425447.
 Alfred Varsady,
"The dissection of sets of polygons,"
Journal of Recreational Mathematics,
vol. 18, no. 4 (198586), pp. 257268.
 Lothar Collatz,
"Strukturen geometrischer Ornamente,"
Journal of Geometry, vol. 31, issue 12 (April 1988), pp. 4264.
 David Paterson,
"Two dissections in 3D,"
Journal of Recreational Mathematics,
vol. 20, no. 4 (1988), pp. 257270.
 Medhat Rahim and Daiyo Sawada.
"Inventing tangrams through dissectionmotion geometry,"
School Science and Mathematics,
vol. 89, no. 2 (February 1989), pp. 113129.
 Alfred Varsady,
"Some new dissections,"Journal of Recreational Mathematics,
vol. 21, no. 3 (1989), pp. 203209.
 David A. Paterson,
"Tdissections of hexagons and triangles,"
Journal of Recreational Mathematics,
vol. 21, no. 4 (1989), pp. 278291.
 M.H. Rahim and D. Sawada,
"The duality of qualitative and quantitative knowing in school geometry,"
International Journal of Mathematical Education in Science and Technology,
vol. 21, issue 2 (1990), pp. 303308.
 Cem Tezer,
"Esparcalama,"
Matematik Dünyasi, vol. 2, no. 5 (1992), pp. 1215.
 Dan Laksov,
"Vilka matematikböcker bör ett gymnasiebibliotek innehalla?,"
Nämnaren nr. 3 (1993), pp. 4148.
 Brian E. Butler,
"Spatial puzzles: A guide for researchers,"
Canadian Psychology, Vol. 35, No. 1, January 1994.
 David A. Paterson,
"Geometric dissections in 4D,"
Journal of Recreational Mathematics,
vol. 28, no.1 (199697), pp. 2237.
 Luc Van den Broeck,
"Twee problemen scharnierend rond een puzzel,"
Wiskunde & Onderwijs, no. 92 (1997), pp. 309317.
 David A. Paterson,
"Enneagon dissections,"
Journal of Recreational Mathematics,
vol. 29, no. 2 (1998), pp. 107113.
 Immaculada Fernández Benito and Encarnación Reyes Iglesias,
"Construcciones y disecciones del octógono,"
SUMA no. 38 (noviembre 2001), pp.6972.
 (Allan Gottlieb),
"Puzzle Corner,"
Technology Review,
2001, no. 5 (December 2001), pp. 3031.
 John Finger,
"Dissections: just fun... or real mathematics?,"
Australian Mathematics Teacher, vol. 58, no. 1 (March 2002), pp. 1718.
 Erik Demaine and Martin Demaine,
"Hinged dissection of the alphabet,"
Journal of Recreational Mathematics, 31(3):204207, 2003.
 Erik D. Demaine, Martin L. Demaine, David Eppstein, Greg N. Frederickson, and Erich Friedman,
"Hinged dissection of polyominoes and polyforms,"
Computational Geometry
vol. 31, Issue 3, June 2005, pp. 237262.
 Tom Verhoeff,
"Figuren opknippen en periodieke vlakvullingen,"
Pythagoras, Jahrgang 45, no. 1 (2005), pp. 1823.
 Antonia Redondo Buitrago and Encarnación Reyes Iglesias,
"La geometría de los polígonos cordobeses (The Geometry of the Cordovan Polygons),"
Visual Mathematics,
issue 104, 2008.
 JeanPaul Delahaye,
"Le géométrie du bricolage,"
Pour la Science,
no. 374 (décembre 2008), pp. 100105.
 Larry Hoehn,
"The isosceles trapezoid and its dissecting similar triangles,"
Forum Geometricorum, vol. 12 (2012) pp. 2938.
 Timothy G. Abbott, Zachary Abel, David Charlton, Erik D. Demaine, Martin L. Demaine, and Scott Kominers,
"Hinged dissections exist,"
Discrete and Computational Geometry,
vol. 47 (2012), pp. 150186.
 Yasuzo Nishimura, Hiroyuki Nyuba, Shinichi Makida, Akira Tsukasake, Naoto Sugimoto, and Masaaki Asakura,
"Investigation contest of mathematics for high school studentsA report of
`H25 The Fukui Science Grand Prix (High school, Mathematics)'",
??, 2014, no. 39, pp. 19.
 JeanPaul Delahaye,
"Dissections géométriques,"
Encyclopaedia Universalis,
consulté le juin 2015.
"L'ouvrage d'Harry Lindgren Recreational Problems in Geometric Dissections and How to Solve Them, par; en 1964, puis complété: et republié en 1972, a longtemps été la référence obligée."
is translated as:
"Harry Lindgren's book Recreational Problems in Geometric Dissections and How to Solve Them, published in 1964 and then completed and republished in 1972, has long been the benchmark."
 Norbert Treitz,
"Teilungen des Dreiecks,"
Spektrum.de, TreitzRätsel/Mathematik/192,
July 6, 2016.
 Norbert Treitz,
"Die Fliesen des Pythagoras,"
Spektrum.de, TreitzRätsel/Mathematik/362,
January 17, 2017.
 P. McMullen,
"Valuations and dissections,"
in ,
edited by P.M. Gruber and J.M. Mills,
Elsevier Science Publishers, Amsterdam, 1993, pp. 739764.
 Rüdiger Thiele,
"Mathematical games,"
in Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences,
Ivor GrattanGuinness, ed.,
Routledge Inc., New York, 1994,
pp. 15551567.
 William L. Schaaf,
A Bibliography of Recreational Mathematics, vol. 3,
National Council of Teachers of Mathematics, 1975.
 George E. Martin,
The Foundations of Geometry and the NonEuclidean Plane,
Springer Undergraduate Texts in Mathematics, New York, 1975.
 Kenneth J. Travers,
Mathematics Teaching,
Harper & Row, 1977.
 Stanley J. Bezuszka, Margaret Kenney, and Linda Silvey,
"Tessellations: the geometry of patterns,"
Creative Publications, 1977.
 Martin Gardner,
Aha! Aha! insight
Scientific American, W.H. Freeman and Company, 1978
 Joseph S. Madachy,
Madachy's Mathematical Recreations,
Dover Publications, 1979.
 Bonnie Averbach and Orin Chein,
Mathematics: Problem Solving Through Recreational Mathematics,
W.H. Freeman, 1980.
 I. J. Schoenberg,
Mathematical Time Exposures,
Mathematical Association of America, 1982.
 Stewart T. Coffin,
Puzzle Craft,
selfpublished, 1985.
 Stewart T. Coffin,
Geometric Puzzle Design,
Taylor & Francis: 1990.
 Branko Grünbaum and G. C. Shephard,
Tilings and Patterns,
W. H. Freeman, New York, 1987.
 Brian Bolt,
Even More Mathematical Activities,
Cambridge University Press, Cambridge: 1987.
 Anton Hanegraaf,
The Delian Altar Dissection,
private publication, Polyhedral Dissections: Elst, the Netherlands, 1989.
 Brian Bolt and David Hobbs,
101 Mathematical Projects,
Cambridge University Press, Cambridge, 1989.
 Stewart T. Coffin,
Puzzling World of Polyhedral Dissections,
1990.
 George E. Martin,
The Foundations of Geometry and the NonEuclidean Plane,
Springer, 1991.
 Martin Gardner,
The Unexpected Hanging and Other Mathematical Diversions,
University of Chicago Press, Chicago, 1991 edition.
 David Wells,
The Penguin Dictionary of Curious and Interesting Geometry,
Penguin Books, London, 1991.
"Harry Lindgren and Greg Frederickson have been responsible for some extraordinary and
beautiful dissections."
"To the puzzlist, the most important feature of a dissection may be the paucity of pieces.
To the mathematician, the exploitation of the natural geometry of each polygon is at least as important.
These dissections possess both of these virtues, plus symmetry and surprise."
 Harold R. Jacobs,
Mathematics: A Human Endeavor,
3rd edition, W.H. Freeman and Company, 1994.
 Martin Gardner,
New Mathematical Diversions,
Mathematical Association of America, Washington, DC, 1995.
 Pieter van Delft and Jack Botermans,
Creative Puzzles of the World,
Key Curriculum Press, Berkeley, CA, 1995.
 Hans Walser,
Symmetrie,
B. G. Teubner, Stuttgart, 1996.
 Claudi Alsina, Carme Burgués, Josep M^{a} Fortuny, Joaquim Giménez, and Montserrat Torra,
Ensenyar matemátiques,
Didáctica de las matemátiques, Barcelona, 1996.
 Herminia Azinián,
Resoluxión de problemas matemáticos:
Visualización con computadora,
Novedades Educatives, Buenas Aires, 1997.
 D. Leites, editor
60odd Years of Moscow Mathematical Olympiads,
Stockholm, Sweden, 1997.
 Carmelo Mammana and V. Villani,
Perspectives on the Teaching of Geometry for the 21st Century: An ICMI Study,
Kluwer Academic Publishers, 1998.
 David Wells,
Geometrinin Gizli Dünyasi (Curious and Interesting Geometry),
Istanbul, Turkey, Birinci Baski, 1998.
 Hans Walser,
Symmetry,
Mathematical Association of America, 2000,
Translation from the German publication.
 Marcel Danesi,
The Puzzle Instinct: The Meaning of Puzzles in Human Life,
Indiana University Press, Bloomington, Indiana, 2002.
 Shailesh Shirali,
Adventures in Problem Solving,
Universities Press, Hyderguda, Hyderabad, India, 2002.
 Eric W. Weisstein,
CRC Concise Encyclopedia of Mathematics,
second edition, CRC Press, 2003.
 David Darling,
The Universal Book of Mathematics, From Abracadabra to Zeno's Paradoxes,
John Wiley and Sons, Hoboken, NJ, 2004.
 Carme Burgues Flamarich,
Matematiques i la seva didactica,
Universitat de Barcelona, 2004.
 David Henderson and Daina Taimina,
Experiencing Geometry: Euclidean and NonEuclidean with History,
Pearson Prentice Hall, 2005.
 Martin Gardner,
aha! A two volume collection: !aha Gotcha, aha! Insight,
Mathematical Association of America, 2006.
Another elegant branch of dissection theory has to do with cutting a given polygon into the smallest number of pieces,
of any shape, that can be rearranged to make a different polygon that is also specified. ...
This field is beautifully covered in
Recreational Problems in Geometric Dissections & How to Solve Them by Harry Lindgren.
 Marcel Danesi,
Labirinti, quadrati magici e paradossi logici,
Edizioni Dedalo, Bari, Italy, 2006.
 Roman Fedorov, Alexei Belov, Alexander Kovaldzhi and Ivan Yaschenko,
Moscow Mathematical Olympiads, 19931999,
Mathematical Sciences Research Institute, American Mathematical Society, 2011.
 Roman Fedorov, Alexei Belov, Alexander Kovaldzhi and Ivan Yaschenko,
Moscow Mathematical Olympiads, 20002005,
Mathematical Sciences Research Institute, American Mathematical Society, 2011.
 Carmelo Mammana and V. Villani,
Perspectives on the Teaching of Geometry for the 21st Century: An ICMI Study,
Springer Science+Business Media: Dordrecht, softcover, 2012.
 Hans Walser,
Symmetrie in Raum und Zeit,
EAGLE, Leipzig, 2014.
 Martin Gardner,
Knots and Borromean Rings, RepTiles, and Eight Queens,
Cambridge University Press, New York, 2014.
 Hans Walser,
EAGLEMALBUCH ZöpfeZerlegungenZehnecke: Geometrische Figuren zum Ausmalen,
Eagle 094, Leipzig 2016.
 ShuYuan Chan,
"Making transformable 3D models",
Airiti Library, (Taiwan?) 2014.
 Jeremy Kilpatrick and Marilyn N. Suydam,
"Reports on Mathematics Education Literature, 19691973",
prepared for Zentralblatt für Didaktik der Mathematik.
 Janet Hudson,
"The University of Pennsylvania Resource Guide to School Mathematics",
Graduate School of Education, University of Pennsylvania, Philadelphia, Pennsylvania, 1974.
 Wayne Peterson,
"Guidelines for grades 912 mathematics curriculum: toward meeting present and future needs",
report IPS62485, Washington Office of the State Superintendent of Public Instruction,
Division of Instructional Programs and Services, May 1985.
 Anton Hanegraaf
"The Delian altar dissection,"
Elst, the Netherlands, 1989.
 John E. Gilbert and Debra S. Carney,
"Bibliography for M333L  Modern Geometry: a Dynamic Approach",
Mathematics Department, University of Texas at Austin.
Spring 2003.
 Associació per promoure i crear un Museu de MAtemàtiques a CAtalunya (MMACA),
"Exposició permanent `Experiències matemàtiques' del MMACA a Cornellà," Barcelona, Catalonia, Spain.
 Alan H. Schoen,
"Set of tiles for covering a surface,"
United States Patent no. 4,223,890, September 23, 1980.
 Haresh Lalvani,
"Periodic and nonperiodic tilings and building blocks from prismatic nodes,"
United States Patent no. 5,575,125, November 19, 1996.
 Haresh Lalvani,
"Nonconvex and convex tiling kits and building blocks from prismatic nodes,"
United States Patent no. 5,775,040, July 7, 1998.
Last updated May 18, 2016.