Origami

4 books rather interesting, a bit different from the usual frog and crane

Polyhedron origami for beginners / Miyuki Kawamura.
Rather interesting constructions using modules. Good explanations and illustrations

Origami monsters & mythical beings / Jay Ansill
Rather complicated although imaginative. Some of the illustrations skip steps.

Modern origami / James Minoru Sakoda

The least interesting of the four. No colour illustrations and fairly boring. But good instructions on how to start with the bases. By modern the author means the style of folding which emphasized the beauty of the straight line and geometric forms. As contrast with older forms as done by Akira Yoshizawa who seek beauty in rounder edges. The author has interesting terms. Eg:
Hikari-Ori (shining light folding) using foil surface, and low relief geometric figures
the eight point star
cross pleating.
This book is rather academic but provides very interesting history of origami.

The art of origami : an illustrated guide to Japanese paperfolding, with over 30 classic designs / Rick Beech

This is the best. Has good explanations, the steps work, tells you latest things, although doesnt show you how to do some of the innovations by Robert Lang.

Some rather interesting points to note:

All origami steps evolve from base folds:
Kite base
Blintz base - derived from Yiddish word for thin pancake containing cheese. The name was taken by Gershon Legman and other 1950s folders to refer to the act of folding all four corners to the centre.
Fish base - from kite base
Waterbomb base
Preliminary base
Bird base - from preliminary base
Frog base - from preliminary base

Some models:
the sampan
the butterfly - there is a Japanese master Akira Yoshizawa who folded numerous different species with many variations
the elephant. There is a group of young Japanese enthusiasts who call themselves the Tantedan and specialize in fairly complex folds. The elephant was designed by a member called Nobuyoshi Enomoto