Within the past few decades, there has been an accelerating development of methods for studying nonlinear equations. Nonlinear analysis offers exciting prospects for certain specific areas of nonlinear problems with continuum mechanics. The objective of this book is to carry out such studies for problems in nonlinear elasticity. This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems. The author's aim is to retain the orientation toward fascinating problems that characterizes the best engineering texts on structural stability while retaining the precision of modern continuum mechanics and employing powerful methods of nonlinear analysis. The author's approach is to lay down a general theory for each kind of elastic body, carefully formulate specific problems, introduce the pertinent mathematical methods, and then conduct rigorous analyses of the problems.