This book contains numerous selected contemporary topics, primarily in Hilbert space, although related extended material in Banach spaces and Riemannian manifolds is also included. A plethora of concrete problems from diverse disciplines are explored, such as: applied mathematics; mathematical biology; chemistry; economics; physics; scientific computing, and engineering. The solutions of such equations can only be found in closed form in special cases; this forces researchers and practitioners to focus on the development of iterative methods to generate a sequence converging to the solutions, provided that some convergence criteria depending on the initial data are satisfied. Due to the exponential development of technology, new iterative methods should be found to improve existing computers and create faster and more efficient ones. We have no doubt that this book will contribute significantly to the enrichment of knowledge and problem solving in the field of Hilbert spaces and related topics.