Lesson 1: The Box
Lesson 2: Box Variation
Lesson 3: The V-Fold
Lesson 4: Box Cut Separately
Lesson 5: Box Tabs and Slots
Lesson 6: V-Fold Tabs and Slots
Lesson 7: Pop Up Words 1
Lesson 8: Pop Up Words 2
Lesson 9: Pop Up Words 3
Lesson 10: Pop Up Words 4
Lesson 11: The X (Slotted Shapes)
Lesson 12: Slotted X with Strap
Lesson 13: Slotted X with Tabs
Lesson 14: Asymmetrical Slotted X
Lesson 15: X Form Cards
Lesson 16: V-Fold Pivot
Lesson 17: Asymmetrical V-Fold Pivot
Lesson 18: 180° Open Top Box
Lesson 19: 180° Box with Closed Top
Lesson 20: 180° Open Top Boat
Lesson 21: 45° Open Box
Lesson 22: Tabletop Floating on Boxes
Lesson 23: Tabletop Floating on I-Beams
My personal favorites! Most are available from Amazon or Book Depository.
If you're only going to buy ONE book about how to make pop ups, I suggest Duncan Birmingham's Pop-Up Design and Paper Mechanics. I waited for years for this revised edition to be published. I loved the first version, but it had been so long out-of-print that I whenever I wanted to read it I had to interlibrary loan the last remaining copy in the state--which is in a prison library. (Begging the question: are prisoners allowed to have craft knives??)
Pop-Up Design and Paper Mechanics: How to Make Folding Paper Sculpture, from Amazon,
or from Book Depository (free shipping worldwide).
Next on my list, especially helpful for those of us who like to see and touch something to see how it works: The Elements of Pop Up by David Carter and James Diaz. This book has working models of the most common pop up mechanisms. I use this as a reference when I want to refresh my memory on the best way to make a specific 3d shape.
Elements Of Pop Up: A Pop Up Book For Aspiring Paper Engineers, from Amazon,
or from Book Depository.
My third go-to book, Making Mechanical Cards by Sheila Sturrock, is not technically all about pop ups, but I believe most people do not really care about the distinction between "pop up cards" and "mechanical cards."
Sturrock's book includes designs I have not seen elsewhere, mostly mechanisms from the great card makers of the past. I am grateful to her for digging up these cards in museums and working out how they were made. She includes full size templates for each mechanism.
Making Mechanical Cards: 25 Paper-Engineered Designs, from Amazon,
or Book Depository.
My top choice for a book about designing sliceforms is John Sharp's Surfaces: Explorations with Sliceforms. I bought this book recently after years of using a mostly trial and error method, with a little help from Sketchup. I learned a lot!
Surfaces: Explorations with Sliceforms, from Amazon, or Book Depository.
If you already have these four, my next purchases would come from this list (some are out-of-print).
The Pop Up Book by Paul Jackson: from Amazon or Book Depository.
Origamic Architecture books by Masahiro Chatani and Keiko Nakazawa.
Paper Engineering & Pop Ups for Dummies by Rob Ives: from Amazon
or Book Depository.
The Pocket Paper Engineer (series) by Carol Barton: from Amazon or Book Depository.
How to Make Super Pop-Ups (or any of her pop up instruction books) by Joan Irvine: from Amazon or Book Depository.
Kirigami: The Art of 3 Dimensional Paper Cutting by Laura Badalucco: from Amazon.
The Art of Paper Folding for Pop Up by Miyuki Yoshida: from Amazon.
Paper Engineering for Pop Up Books and Cards or Up Pops by Mark Hiner: from Amazon.
Full Disclosure: I received no compensation from any of these authors or publishers, nor any complementary review titles.