This book provides an introduction to the mathematical aspects of Euler's 
elastic theory and its application. The approach is rigorous, as well as 
visually depicted, and can be easily digested. The first few chapters introduce 
the needed mathematical concepts from geometry and variational calculus. The 
formal definitions and proofs are always illustrated through complete 
derivations and concrete examples. In this way, the reader becomes acquainted 
with Cassinian ovals, Sturmian spirals, co-Lemniscates, the nodary and the 
undulary, Delaunay surfaces, and their generalizations. The remaining chapters 
discuss the modeling of membranes, mylar balloons, rotating liquid drops, Hele-
Shaw cells, nerve fibers, Cole's experiments, and membrane fusion. The book is 
geared towards applied mathematicians, physicists and engineers interested in 
Elastica Theory and its applications.