This book lays a unique and straightforward mathematical foundation on the aspects of liquid layers, capillary interfaces, floating drops and particles. For the first time, these topics are studied in a joint framework. Readers will acquire deeper comprehension and gain results. Practical interest are presented, making it beneficial to engineers and physicists as well as mathematicians.The text takes an insight-oriented approach that gives it immediacy and flexibility. It contains 70 problems where some are exercises, while others are open problems. It is also illustrated with 95 figures and photographs for further understanding.