Symmetry

Traditional viewpoint

Higher symmetry is related to higher order, less entropy and less stability (See many textbooks of statistical mechanics. Particularly "Order out of Chaos" book by Prigogine school of thermodynamics)

Higher symmetry, higher entropy

Joe Rosen

"The symmetry group of the cause is a subgroup of the symmetry group of the effect" -Curie's symmetry principle, is developed further by Rosen. Rosen, J. Symmetry in Science; Springer: New York, 1995; p. 191

Shu-Kun Lin

Higher symmetry-higher entropy-higher stability relation was set up from a new approach:
Lin, S. -K. Correlation of Entropy with Similarity and Symmetry. Journal of Chemical Information and Computer Sciences, 1996, 36, 367-376, and citations (Reprints are available). http://http://www.mdpi.org/lin/lin-rpu.htm

Curie's symmetry principle has been proved by Lin's "higher similarity-higher entropy" relation (similarity principle) and the second law of thermodynamics.

"The highest level of symmetry is total chaos" and "A gas has more symmetry than a liquid, and a liquid more symmetry than a solid"
Chapter 13 of my book in progress, "Atomic Reality: The Simplest of All Possible Worlds" entitled "Symmetry, Simplicity, and Natural Law" is now available for comments at 

Symmetry is in principle ugly

Symmetry is in principle ugly because it is related to entropy and information loss
Lin, S. -K. Correlation of Entropy with Similarity and Symmetry. Journal of Chemical Information and Computer Sciences, 1996, 36, 367-376, and citations (Reprints are available). http://http://www.mdpi.org/lin/lin-rpu.htm

Frequently cited books on symmetry

Hermann Weyl, Symmetry, Princeton UP, 1952, innumerable reprintings.

Symmetry definition

The word symmetry comes from the Greek "symmetria", meaning "the same measure".- Symmetry, A Unifying Concept by Magdolna Hargittai, Shelter Publications, Inc., Bolinas, California, 1994 (p.XII, preface)
Also, http://www.symmetry.org/, and section 6 in Entropy 2003, 5[3], 271-312

Icke, V. The Force of Symmetry, Cambridge University Press, Cambridge, 1995, p.173.
Will the Universe live forever? ... The danger lies not in the need for absolute amounts of energy, but in the availability of energy differences. If there did not exist, everything would be in equilibrium and life would be impossible.

Elliott, J.P. and Dawber, P. G. (1979) Symmetry in Physics, Macmilan, London
This was the text book I used when I was learning group theory in 1982-1983 (two semesters at the physics department of China University of Science and Technology).
According to the Concise Oxford Dictionary, symmetry is defined as '(Beauty resulting from) right proportion between the parts of the body or any whole, balance, congruity, harmony, keeping'.  [p1].