This book deals with especially difficult problems in theoretical physics. This book suggests original approaches, which may lead to new directions of research. This book explores the problem of three interacting bodies, with application to the motion of the Sun, Earth and Moon. The solution of the many-body motion is analyzed, and new ways of investigating it are suggested. The ferromagnet-superconductor junction is analyzed thoroughly, with applications in the modern spintronics. Quantum beats in the decay rate of positronium in matter are investigated, highlighting the possibility of detecting local magnetic interactions. A large part of the book is dedicated to the study of electrolytes, especially in their high-concentration limit, with relevance to the modern investigations of the ionic liquids. An analysis is presented of the quantization problem in curved spaces, by means of an original approach. Finally, the role played by the interaction in neutrino oscillations is discussed. Hopefully, the original approaches presented in this book may help lead to new ways of investigating such interesting phenomena. This book is addressed to science students and researchers with an interest in exploring new ways in the physical sciences.