This reprint MDPI edition comprises papers drawn from the Special Issue entitled "Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms". This Special Issue includes research papers which cover a wide range of topics in classical, computational and applied mathematics: differential equations, especially concerning singular solutions and coefficients; transmutation theory with all kinds of its applications; integral transforms and special functions theory; classical and advanced inequalities; and numerical methods for all the abovementioned problems.