The book compiles papers presented at the International Conference 'Advances in Applications of Analytical Methods in Solving Differential Equations', held in honour of Academician Lev V. Ovsiannikov's 105th birthday anniversary. This collection reflects his extensive contributions to the theory of differential equations, modelling, and the application of analytical methods. In addition to classical methods such as analytical integration of systems of equations and their applications in various fields of Science and Engineering, the book explores new areas of research. This includes the application of group analysis to novel mathematical models and nonlinear problems, particularly equations with nonlocal terms (symmetries of difference and differential equations, as well as fractional differential equations). One of the notable contributions in the book is the development of a Hamiltonian approach for delay differential equations, representing a novel area of research that has not been previously explored. The book is anticipated to appeal to a broad audience of experts in applied mathematics, fluid dynamics, and modelling, as well as to young scientists and graduate students interested in the analysis of nonlinear equations.